🧠📚 Mitch's Mind Tangle
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Abelianization
associated vector bundle
cone over space
constant rank theorem
equivariant rank theorem
fixed point set
frontier condition
locally finite decomposition
orbit stabilizer theorem
orbit type stratification
Poisson transversal
principal orbit type theorem
principal stratum of symplectic manifold
proper group action
reduction in stages
relatively open set
Sard's theorem
shifting trick for symplectic reduction
stratified symplectic space
stratified topological space
Weyl chamber
Whitney Approximation Theorem
Whitney Embedding Theorem
Brocker - Dieck
quaternion
symplectic group
DaSilva
conormal bundle
cotangent lift
de Rham cohomology
de Rham theorem
differential of a function
Euler-Lagrange equations
generating function
Hamilton's equations
integral of differential form
isotopy
Lagrangian submanifold
line integral
normal bundle
Stokes theorem
symplectic potential
symplectic volume
tautological form
time dependent vector field
tubular neighborhood theorem
Economics
Finance
ACE simulation with subjective prices
Carry charge hedge
Finance
OHMC with Approx Bayesian Comp
Pure risk avoidance hedging
Risk neutral density
Stacked synthetic storage strategy
Subjective asset pricing
subjective distribution
Subjective OHMC
synthetic refining strategy
Synthetic storage strategy
Austrian economics
choice architecture active inference
communication system advances human knowlege
dynamic choice set
Economics
Efficient Market Hypothesis
entrepreneurship adoption and state space
entrepreneurship and active inference
models and knowledge
Neoclassical Equilibrium
Problems with utility based choice models
Society members as observations
Hatcher
CW complex
weak topology
Literature
10: The Market Order or Catallaxy
A step-by-step tutorial on active inference and its application to empirical data
Active inference and agency: optimal control without cost functions
Active inference: The free energy principle in mind, brain, and behavior
Algebra: Chapter 0
Algebraic topology
An introduction to Bayesian network theory and usage
An Introduction to the Bootstrap
Analysis of integrated and cointegrated time series with R
Bayesian Model Comparison and Validation
Bayesian networks: An introduction
Bayesian Specification Analysis in Econometrics
Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician
Chapter 2: The Low Road to Active Inference
De Finetti was Right: Probability Does Not Exist
Economics and knowledge
Entrepreneurship and economic growth: The theory of emergent institutions.
Foundations of mechanics
Gelfand–Cetlin abelianizations of symplectic quotients
Hedge your monte carlo
Hedging in the theory of corporate finance: A reply to our critics
How to take smart notes: One simple technique to boost writing, learning and thinking
Insurance: Don't Sweat the Small Stuff
Introduction to Modern Bayesian Econometrics
Introduction to smooth manifolds
Introduction to smooth manifolds
Introduction to symplectic topology
Keynote: Dr. Stephen Wolfram
Lack of confidence in approximate Bayesian computation model choice
Learning, estimation, and the stability of rational expectations
Lectures on poisson geometry
Lectures on symplectic geometry
Market Models: A Guide to Financial Data Analysis
Mathematical Statistics and Data Analysis
Measure, integration & real analysis
METALLGESELLSCHAFT AND THE ECONOMICS OF SYNTHETIC STORAGE
Non-abelian convexity by symplectic cuts
Non-abelian convexity by symplectic cuts
Nudge: The final edition
Numbers as a cognitive and social technology: on the nature of conventional number sequences used in economic systems
On Discriminative vs. Generative Classifiers: A comparison of logistic regression and naive Bayes
Probabilistic Graphical Models: Principles and Applications
Representations of compact lie groups
Retrospect and Prospect
Riemannian geometry
Risk transfer: derivatives in theory and practice
Stratified symplectic spaces and reduction
Symposium on current views of subjective probability: Subjective probability as the measure of a non-measurable set
The local structure of Poisson manifolds
The math is not the territory: navigating the free energy principle
The normal form theorem around Poisson transversals
Topics in differential geometry
Value at Risk: Uses and Abuses
What Should Economists Do?
Math
(left) resolution of R-module
(local) coframe
(local) frame
$\sigma$-algebra
$\sigma$-algebra closed under countable intersection
1-parameter subgroup
abelian group
action
action of fundamental group on cover
action-angle coordinates
adjoint representation of Lie algebra
adjoint representation of Lie group
affine algebraic group
affine algebraic variety
affine connection
affine scheme
algebra homomorphism
algebra ideal
algebra of invariants
algebraic closure
algebraic extension
algebraic geometry
algebraic numbers
algebraic structures
algebraic topology
algebraically closed field
annihilator of module
annihilator of vector space
approximation by simple functions
Artin-Wedderburn theorem
associative algebra
basis for exterior product
basis for tangent space of manifold
bialgebra
bimodule
Bolzano-Weierstrass Theorem
Borel $\sigma$ algebra
Borel measurable function
boundary of chain complex
boundary of set
bounded convergence theorem
Cartan's magic formula
categorical quotient
category
category theory
Cayley-Hamilton theorem
center of a ring
chain complex
chain homotopy
chain map
character of group representation
characteristic polynomial
chart
Christoffel symbol
class
class function
classical analysis
closed subgroup theorem
closure of set
coalgebra
cofinite topology
coisotropic subspace
commutator subgroup
commuting vector fields
compact space
complete vector field
completely integrable system
conformal metric
continuity with limsup
continuous functions and basis
continuous map
coordinate ring
cotangent bundle
cotangent space
covering space
cumulative distribution function
curve
cycle of chain complex
cyclic module
Darboux thoerem
De Morgan's law
defining map
deformation retract
degree of extension
density function
derivation
diffeomorphism
differences between Riemann and Lebesgue integral
differential
differential form
differential geometry
direct product (groups)
direct sum
Directed acyclic graph (DAG)
Dirichlet function
discrete topology
distribution of random variable
division ring
domain (algebra)
domain (ring theory)
dominated convergence theorem
dual basis
dual space
effective action
Egorov's Theorem
embedded submanifold
equivalence of reduced algebras and affine sets
equivalent categories
equivariant map
equivariant map
essentially surjective
Euclidean topology
exact complex
exact sequence
excision theorem
expected value
exponent of module
exponential map
extension module
exterior algebra
exterior derivative
exterior power
faithful functor
fiber bundle
field
field characteristic
field extension
field of fractions
finite complement topology
finitely generated algebra
finitely generated extension
first isomorphism theorem
flat R-module
flow
foliation
free group
free group action
free product (groups)
free R-module
free resolution
Frobenius theorem
full functor
functor
fundamental group
Fundamental Theoreom on Flows
fundamental vector fields
general linear group
generalized orthogonal group
generated submodule
graded abelian group
graded algebra
graded ring
graph
group
group action
group homomorphism
group representation
group ring
Group theory
Hamiltonian action
Hamiltonian G-space
Hamiltonian torus actions and integrable systems
Hamiltonian vector field
Hausdorff space
Hilbert Basis Theorem
Hilbert's finiteness theorem
homeomorphism
homogeneous space
homology
homotopy
homotopy equivalence
homotopy equivalent complexes
homotopy group
Hurewicz theorem
ideal (ring theory)
idempotent
immersion
Implicit function theorem
independence (probability)
induced measure
induced Riemannian metric
induced subgroup from cover
infinitesimal generator
injective R-module
inner product
integral curve
integral leaks
integral manifold
interior of set
interior product
invariant function
invariant subset
Inverse function theorem
inverse limit
involutive distribution
irreducible representation
isomorphism
isotropic subspace
Jacobson radical
Jordan canonical form
Kolmogorov's 0-1 law
Lagrangian subspace
Lebesgue integrability
Lebesgue integral
Lebesgue measurable
Lebesgue measure
Lebesgue number lemma
left-invariant vector field
level set
Levi-Civita connection
Lie algebra
Lie algebra action
Lie algebra of a Lie group
Lie algebra representation
Lie bracket
Lie derivative
Lie group
Lie group representation
Lie theory
Lie's third theorem
lifting criterion for continuous maps
linear algebra
linear symplectomorphism
local ring
localization at a prime ideal
localization of a module
localization of a ring
locally free
long exact sequence of homology
loop
lower Lebesgue sum
lower limit topology
Luzin's Theorem
Marsden-Weinstein symplectic reduction theorem
Maschke lemma
Math
matrix exponential
matrix Lie algebra
maximal ideal
maximal smooth atlas
maximal spectrum
Mayer-Vietoris Theorem
measure
measure space
Measure theory
measureable function
metric
metric topology
minimal polynomial
module on sheaf
module over ring
moment map
Monotone Convergence Theorem
monotone convergence theorem (integral version)
multi-vector fields
multiplicative subset
multiplicity of representation
Nakayama's Lemma
natural transformation
nested interval theorem
nilradical of ring
Noetherian R-module
Noetherian ring
normal subgroup
not Lebesgue integrable function
not Riemann integrable function
Nullstellensatz
open map
opposite category
opposite ring
orbit
orbit space
orbits as submanifolds
orthogonal family of central idempotents
orthogonal group
outer measure
partially ordered set
partition of unity
path
path lifting lemma
period (of module)
PID modules
Poincare lemma
Poincare-Birkhoff-Witt theorem
Poisson algebra
Poisson bracket
Poisson bracket on symplectic manifold
Poisson commute
Poisson manifold
Poisson map
polynomial ring
presentation of a group
prime ideal
prime spectrum
prime subfield
principal bundle
principal ideal domain
probability space
Probability theory
projective R-module
projective resolution
proper map
quotient group
quotient manifold theorem
quotient map
quotient ring
quotient topology
R-algebra
R-module
radical of an ideal
random variable
rank of smooth map
rational canonical form
reduced homology
reduced ring
reductive group
regular
regular cover
regular distribution
regular value
regular value theorem
related vector fields
relative singular homology
representation theory
representation theory of finite groups
retract
Reynolds operator
Ricci curvature tensor
Riemann curvature
Riemann integrability
Riemann integral
Riemann lower/ upper sum
Riemannian metric
ring
ringed space
scalar curvature
Schouten bracket
Schur's Lemma
second countable
section
sectional curvature
Seifert-Van Kampen Theorem
semilocally simply connected
semisimple module
semisimple ring
sheaf
short exact sequence
simple field extension
simple function
simple graph
simple module
simplex
simply connected space
singular distribution
singular homology
singular point
singular value
skeleton
skyscraper sheaf
slice chart
smallest $\sigma$-algebra
smooth bump function
smooth embedding
smooth function
smooth manifold
smooth map
space of all vector fields
special linear group
stabilizer
stereographic projection
stock
submersion
subspace topology
symmetric power
symplectic action
symplectic complement
symplectic geometry
symplectic leaf
symplectic manifold
symplectic vector field
symplectic vector space
symplectic vector subspace
symplectomorphism
tail field
tangent bundle
tangent space
tensor algebra
tensor coordinate matrix
tensor field
tensor product
tensor rank
topological basis
topological embedding
topological group
topological manifold
topological pair
topology
topology generated by basis
Tor group
torsion (module theory)
torsion of affine connection
torus (topology)
trace
transitive group action
unitary group
universal cover
universal cover criterion
universal enveloping algebra
vanishing locus
vector bundle
vector field
vector space
vector space as a k-module
vector space as an affine variety
velocity vector of curve
Vitali set
weak Nullstellensatz
Weak product (group)
Weinstein splitting theorem
Zariski topology
Zariski's Lemma
Zorn's lemma
MATH 6360 - Lie theory
derived series
Lie algebra ideal
lower central series
nilpotent Lie algebra
quotient Lie algebra
radical of a Lie algebra
second isomorphism theorem
semidirect product
semidirect product (Lie algebra)
semisimple Lie algebra
simple Lie algebra
solvable Lie algebra
Stats
Bayesian
2 model posterior odds
Approximate Bayesian Computation (ABC)
Bayes Factor
Bayes net criteria
Bayesian interval and non-measureable
Bayesian network
Bayesian network joint probability
Bayesian prediction algorithm
Bayesian Specification Test
Bayesian statistics
Bayesian surprise
Honesty of Bayesian inference
Likelihood ratio - frequentist
Likelihood ratio vs. Bayes factor
MC and BN
Posterior odds on a model
Posterior prediction vs. parametric bootstrap
Posterior Predictive Distribution
Predictive distribution
Simulating distribution
Simulating sample predictions from test data
Time series
AR time series model
ARMA time series models
Autocovariance
detrending series
integrated process
MA time series
Mean reversion
Second Order Stationary
stability of VAR model
Stationary time series
Trend-stationary process
VAR model
VAR model
VECM - time series
active inference in behavioral economics
conditional independence
Convergence of stationary MC
Criticisms of MLE
Discriminative model
expected free energy
generative model
graph of HMM
Hidden Markov Model (HMM)
Markov chain
Markov chain matrix
Markov property
Maximum Likelihood Estimator (MLE)
Monte Carlo Markov chain
Parametric Bootstrap
Probabilistic Graphical Model (PGM)
rejection sampling
Stationary MC distribution
Statistics
surprise (statistical)
variational free energy
Connection is crucial
pullback of differential form
reading as a process
Home
❯
MATH 6360 Lie theory
❯
second isomorphism theorem
second isomorphism theorem
Oct 09, 2025
2 min read
todo
For groups
For Lie algebras
If
is a
Lie algebra
and if
and
are
ideals
in
such that
then
Proof
todo
Graph View
Table of Contents
For groups
For Lie algebras
Proof
Backlinks
radical of a Lie algebra