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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. [85%] 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) [85%] 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. [85%] 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. [85%] 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) [85%] 2024-01-01
7. 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
8. 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]
9. 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) [70%] 2023-12-15
10. 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 ... [70%] 2023-11-17
11. 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) [70%] 2023-12-28 [Chinese superheroes] [Iron Fist (comics)]...
12. 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]
13. 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]
14. 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]
15. Affine Lie algebra: In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. It is a Kac–Moody algebra for which the generalized Cartan matrix is ... [69%] 2022-05-04 [Lie algebras] [Representation theory]...
16. Parabolic Lie algebra: In algebra, a parabolic Lie algebra \displaystyle{ \mathfrak p }[/math] is a subalgebra of a semisimple Lie algebra \displaystyle{ \mathfrak g }[/math] satisfying one of the following two conditions: These conditions are equivalent over an algebraically closed field of characteristic ... [69%] 2022-07-21 [Lie algebras]
17. Lie algebra bundle: In mathematics, a weak Lie algebra bundle is a vector bundle \displaystyle{ \xi\, }[/math] over a base space X together with a morphism which induces a Lie algebra structure on each fibre \displaystyle{ \xi_x\, }[/math]. A Lie algebra bundle \displaystyle ... (Concept in topology (mathematics)) [69%] 2023-05-19 [Algebraic topology] [Complex analysis]...
18. Lie algebra, exponential: Lie algebra of type $ ( E) $ A finite-dimensional real Lie algebra $ \mathfrak g $ for any element $ X $ of which the operator of adjoint representation (cf. Adjoint representation of a Lie group) $ \mathop{\rm ad} X $ does not have purely imaginary ... (Mathematics) [69%] 2023-10-18
19. Lie algebra extension: In the theory of Lie groups, Lie algebras and their representation theory, a Lie algebra extension e is an enlargement of a given Lie algebra g by another Lie algebra h. Extensions arise in several ways. (Physics) [69%] 2023-04-28 [Lie groups] [Quantum field theory]...
20. Restricted Lie algebra: In mathematics, a restricted Lie algebra is a Lie algebra together with an additional "p operation." Let L be a Lie algebra over a field k of characteristic p>0. A p operation on L is a map X ↦ X ... [69%] 2023-07-25 [Algebraic groups] [Lie algebras]...