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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. 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. [84%] 2024-01-20
3. 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) [84%] 2024-01-01 [Lie groups] [Lie algebras]...
4. 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. [84%] 2023-01-25 [Lie algebras]
5. Lie algebra: A Lie algebra is an easy example of an algebraic structure that is not associative. Lie algebras describe infinitesimal symmetries or transformations. [84%] 2023-07-30 [Physics] [Mathematics]...
6. 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) [84%] 2024-01-01
7. 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
8. 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
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. 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]
13. Classical Lie algebras: The classical Lie algebras are finite-dimensional Lie algebras over a field which can be classified into four types \displaystyle{ A_n }[/math], \displaystyle{ B_n }[/math], \displaystyle{ C_n }[/math] and \displaystyle{ D_n }[/math], where for \displaystyle{ \mathfrak{gl}(n) }[/math] the ... [75%] 2025-03-23 [Algebra] [Lie algebras]...
14. 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
15. Glossary of Lie groups and Lie algebras: This is a glossary for the terminology applied in the mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory of Lie groups and Lie algebras, see Glossary of representation theory. (none) [70%] 2024-10-01 [Glossaries of mathematics] [Lie algebras]...
16. Lin Lie: Lin Line (林烈) es un superhéroe Chino que aparece en los cómics americanos publicados por Marvel Comics. Lin apareció por primera vez en la web manhua Warrior of the Three Sovereigns (chino simplificado: 三皇斗战士) #1 (mayo de 2018) como Sword Master, un descendiente ... [69%] 2023-11-17
17. Lin Lie: Lin Lie (Chinese: 林烈) is a Chinese superhero originally appearing in web manhua and later American comic books published by Marvel Comics. Created by artist Gunji and writer Shuizhu, Lin first appeared in the Chinese digital series Warrior of the Three ... (Fictional superhero in Marvel Comics) [69%] 2023-12-28 [Chinese superheroes] [Iron Fist (comics)]...
18. Lie algebra, graded: A Lie algebra $ \mathfrak g $ over a field $ K $ that is graded by means of an Abelian group $ A $, that is, which splits into a direct sum of subspaces $ \mathfrak g _ \alpha $, $ \alpha \in A $, in such a way ... (Mathematics) [69%] 2023-10-13 [Nonassociative rings and algebras]
19. Lie algebra, exceptional: A simple Lie algebra (see Lie algebra, semi-simple) that is not classical. Over an algebraically closed field of characteristic zero there are 5 exceptional Lie algebras: $E_6$, $E_7$, $E_8$, $F_4$, and $G_2$, of dimension 78, 133, 248, 52, and ... (Mathematics) [69%] 2023-10-17 [Nonassociative rings and algebras]
20. Quasi-Lie algebra: In mathematics, a quasi-Lie algebra in abstract algebra is just like a Lie algebra, but with the usual axiom replaced by In characteristic other than 2, these are equivalent (in the presence of bilinearity), so this distinction doesn't ... [69%] 2023-05-19 [Lie algebras]