In the case of Lie superalgebras which are defined as $L=L_{\bar{0}} \oplus L_{\bar{1}}$, I am a bit confused about the term "homogeneous subalgebra". Does it mean that the subalgebra which is generated by, for instance, $A \subseteq X_{\bar{0}}$, where $ X_{\bar{0}}$ are generators of degree zero is a homogeneous subalgebra? Thank you for your time.
2025-01-13 08:03:51.1736755431
homogeneous subalgebra of a Lie superalgebra
28 Views Asked by Nil https://math.techqa.club/user/nil/detail AtRelated Questions in LIE-ALGEBRAS
- How do I make sense of terms $X^j\partial_j(Y^i)$ in the Lie bracket of vector fields?
- When derivations are exactly homomorphisms?
- Ideals in Lie algebras
- Lie bracket on $\Gamma(TM\oplus (M\times \mathfrak{g}))$?
- 2-dimensional derived subalgebra of 3-dimensional Lie algebra is abelian
- How are groups with the same Lie Algebra inequivalent?
- Generators of a semi simple lie algebra must be traceless
- From Generators of Lie Groups to Representations
- How does a Lie algebra act on a tensor product of L-modules?
- Representation of a Kac-Moody algebra
Related Questions in GRADED-ALGEBRAS
- Filtration on commutative algebra
- Banach space decomposition
- Equality of localization of homogeneous ideal by a variable $x_i$.
- On the $k$-vector space dimension of graded pieces of an Artinian $k$-algebra $k[x,y]/J$
- Definition of Homomorphism of $I$-Graded Vector Spaces
- Definition of Graded Algebra
- Hilbert-Samuel multiplicity of standard graded $k$-algebra which is an integral domain and $k$ is algebraically closed
- On an analogy of the highest generating degree and reduction of ideals
- Symbolic Rees Algebra of an ideal in a Noetherian excellent ring
- Computation of Associated Graded Module
Related Questions in SUPERALGEBRA
- When are minimal faithful modules over algebras unique?
- Finite dimensional, irreducible representations of the Lie superalgebra gl(1|1)
- How is this algebra a superalgebra?
- Best texts on supermathematics for a mathematician?
- Is the exterior algebra a universal enveloping superalgebra?
- $\mathbb{Z}_2-$grading by Hodge star operator.
- Can $\mathfrak{so}(3,1) \sim \mathfrak{sl}_2(\mathbb{C})$ be supersymmetrized?
- A question about super vector space
- A Grassmann-Variable Identity from Wikipedia
- What is contragredient about contragrediant Lie superalgebras
Related Questions in FREE-LIE-ALGEBRA
- Defining a filtration on free Lie algebra in terms of generators
- Algorithm for decomposing an element of a free Lie algebra in terms of Hall basis
- Jacobi identity, free nilpotent Lie algebra
- Basis of free Lie-algebra through Lazard-elimination
- Is every solvable algebras are nilpotent?
- Intuition for Kozsul algebras/Lie algebras
- properties of canonical algebra homomorphism $\varphi:U(L(A))→A$ for $A$ commutative, associative algebra
- Description of free Lie algebra in Weibel's book
- Free Lie algebra over the set $X=\{x\}$
- About finitely presented algebras and free product
Related Questions in LIE-SUPERALGEBRAS
- Is the exterior algebra a universal enveloping superalgebra?
- Fundamental representations of Lie superalgebras
- What is contragredient about contragrediant Lie superalgebras
- How to obtain all classical simple Lie superalgebras of rank 2?
- one dimensional Lie superalgebras
- existence of a Lie superalgebra with unsolvable word problem
- homogeneous subalgebra of a Lie superalgebra
- General commutators of derivations of the exterior algebra
- super commutation of matrices
- Coordinate superalgebra
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity