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1. Lie algebra, algebraic: The Lie algebra of an algebraic subgroup (see Algebraic group) of the general linear group of all automorphisms of a finite-dimensional vector space $V$ over a field $k$. If $\mathfrak g$ is an arbitrary subalgebra of the Lie algebra ... (Mathematics) [100%] 2023-10-17
2. Representation theory of semisimple Lie algebras: In mathematics, the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory was worked out mainly by E. [90%] 2024-06-03 [Lie algebras]
3. Lie-Algebra: Eine Lie-Algebra (auch Liesche Algebra), benannt nach Sophus Lie, ist eine algebraische Struktur, die mit einer Lie-Klammer versehen ist, d. h., es existiert eine antisymmetrische Verknüpfung, die die Jacobi-Identität erfüllt. [85%] 2024-01-20
4. Lie algebra: In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space \displaystyle{ \mathfrak g }[/math] together with an operation called the Lie bracket, an alternating bilinear map \displaystyle{ \mathfrak g \times \mathfrak g \rightarrow \mathfrak g }[/math], that satisfies the ... (Algebraic structure used in analysis) [85%] 2024-01-01 [Lie groups] [Lie algebras]...
5. Lie- algebra: In mathematics, a Lie-* algebra is a D-module with a Lie* bracket. They were introduced by Alexander Beilinson and Vladimir Drinfeld ((Beilinson Drinfeld)), and are similar to the conformal algebras discussed by (Kac 1998) and to vertex Lie algebras. [85%] 2023-01-25 [Lie algebras]
6. Lie algebra: A Lie algebra is an easy example of an algebraic structure that is not associative. Lie algebras describe infinitesimal symmetries or transformations. [85%] 2023-07-30 [Physics] [Mathematics]...
7. Lie algebra: A Lie algebra is a unitary $k$-module $L$ over a commutative ring $k$ with a unit that is endowed with a bilinear mapping $(x,y)\mapsto [x,y]$ of $L\times L$ into $L$ having the following two properties ... (Mathematics) [85%] 2024-01-01
8. Lie algebra of an algebraic group: l0584801.png ~/encyclopedia/old_files/data/L058/L.0508480 104 0 104 The analogue of the Lie algebra of an analytic group, which relates to the case of affine algebraic groups. As in the analytic case, the Lie algebra of an ... (Mathematics) [83%] 2023-12-15
9. Lie algebras, variety of: over a ring $ k $ A class $ \mathfrak V $ of Lie algebras (cf. Lie algebra) over $ k $ that satisfy a fixed system of identities. (Mathematics) [80%] 2024-01-01
10. Glossary of Lie algebras: This is a glossary for the terminology applied in the mathematical theories of Lie algebras. The statements in this glossary mainly focus on the algebraic sides of the concepts, without referring to Lie groups or other related subjects. [80%] 2024-01-01 [Glossaries of mathematics] [Lie algebras]...
11. Cohomology of Lie algebras: A special case of cohomology of algebras. Let $ \mathfrak G $ be a Lie algebra over a commutative ring $ K $ with an identity, and suppose that a left $ \mathfrak G $- module $ V $ has been given, that is, a $ K $- linear representation ... (Mathematics) [80%] 2023-10-22
12. Algebraic algebra: An algebra with associative powers (in particular, an associative algebra) over a field in which all elements are algebraic: an element $a$ of the algebra $A$ is called algebraic over the field $F$ if the subalgebra $F$ generated by $a ... (Mathematics) [80%] 2023-10-13
13. Algebraic theory: Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. [79%] 2023-12-31 [Mathematical logic]
14. Algebraic theory: Informally in mathematical logic, an algebraic theory is a theory that uses axioms stated entirely in terms of equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. [79%] 2023-12-31 [Mathematical logic]
15. Linear Lie algebras: A linear (or "classical") Lie algebras is a Lie algebra whose elements can be represented as matrices (or linear transformations over some vector space over a field. See also: sl(n) (special linear Lie algebra) An A-series Lie algebra ... [75%] 2023-11-07 [Lie algebra]
16. Theory of Lie groups: In mathematics, Theory of Lie groups is a series of books on Lie groups by Claude Chevalley (1946, 1951, 1955). The first in the series was one of the earliest books on Lie groups to treat them from the global ... [75%] 2023-10-08 [Mathematics books] [Lie groups]...
17. Fundamental theorem of algebraic K-theory: In algebra, the fundamental theorem of algebraic K-theory describes the effects of changing the ring of K-groups from a ring R to \displaystyle{ R }[/math] or \displaystyle{ R[t, t^{-1}] }[/math]. The theorem was first proved by ... (On the effects of changing the ring of ''K''-groups) [74%] 2023-12-31 [Algebraic K-theory] [Theorems in algebraic topology]...
18. Representation theory of Hopf algebras: In abstract algebra, a representation of a Hopf algebra is a representation of its underlying associative algebra. That is, a representation of a Hopf algebra H over a field K is a K-vector space V with an action H ... [72%] 2023-11-22 [Hopf algebras] [Representation theory]...
19. Weil algebra of a Lie algebra: Let $G$ be a connected Lie group with Lie algebra $\frak g$. The Weil algebra $W ( \mathfrak{g} )$ of $\frak g$ was first introduced in a series of seminars by H. (Mathematics) [71%] 2023-10-19
20. Automata, algebraic theory of: A branch of the theory of automata (cf. Automata, theory of) in which algebraic tools are employed in the study of automata. (Mathematics) [71%] 2023-12-31