Superalgebra - Wikipedia
WebIn mathematics and theoretical physics, a superalgebra is a Z2 - graded algebra. [1] . That is, it is an algebra over a commutative ring or field with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading. The prefix super- comes from the theory of supersymmetry in theoretical physics.
Superalgebra - Encyclopedia of Mathematics
WebMar 31, 2020 · Superalgebra. A $ \mathbf Z / 2 $- graded algebra over a field $ k $ ( see Graded algebra ), i.e. a super-space $ A $ over $ k $ endowed with an even linear mapping $ A \otimes A \rightarrow A $. A superalgebra is said to be commutative (graded-commutative or supercommutative) if.
WebDefinition 1.2.A Lie superalgebra is a super vector space g = g 0 ⊕g 1 with a Z 2−graded bilinear operation [−,−] : g×g →g such that for all homogeneous elements a,b,c (1)Skew-supersymmetry: [a,b] = −(−1)|a|·|b|[b,a] (2)Super Jacobi identity: [a,[b,c]] = [[a,b],c] + (−1)|a|·|b|[b,[a,c]] Remark. If g = g
Superalgebra - an overview | ScienceDirect Topics
WebA superalgebra is a super vector space whose elements can be multiplied together in such a way that the product of an even element with an even element and that of an odd element with an odd element are both even, while the product of an odd element with an even element is odd; more formally:
Lie superalgebra - Wikipedia
WebIn mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2 ‑ grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry.
Lie Superalgebra - an overview | ScienceDirect Topics
WebLie Superalgebra. The Lie superalgebra associated with the associative superalgebra, Hom(V ) (by introducing the bracket [, ] as defined above) is denoted as pl(V ) called the general linear Lie superalgebra of V. From: Introduction to Finite and Infinite Dimensional Lie (Super)algebras, 2016. Related terms: Lie Algebra; Homomorphism; G-Module ...
WebDefinition 1.2.A Lie superalgebra is a super vector space g = g 0 ⊕g 1 with a Z 2−graded bilinear operation [−,−] : g×g →g such that for all homogeneous elements a,b,c (1)Skew-supersymmetry: [a,b] = −(−1)|a|·|b|[b,a] (2)Super Jacobi identity: [a,[b,c]] = [[a,b],c] + (−1)|a|·|b|[b,[a,c]] Remark. If g = g
WebPhysics. by Springer-Verlag 1977. A Sketch of Lie Superalgebra Theory. V. G. Kac. Moscow Institute for Electronics Equipment, Moscow, USSR. Abstract. This article deals with the structure and representations of Lie superalgebras (Z2-graded Lie algebras). The central result is a classification of simple Lie superalgebras over IR and C. Introduction.
WebWe introduce the concept of a δ-superderivation of a superalgebra. δ-Derivations of Cartan-type Lie superalgebras are treated, as well as δ-superderivations of simple finite-dimensional Lie superalgebras and Jordan superalgebras over an algebraically closed field of characteristic. 0. We give a complete description of 1 2-derivations.
WebA superalgebra S is ZTgraded if it is decomposed into a direct sum of m+n+l subspaces G i (i=-n, -n+l .... 0,I .... m) such that S =~G i i, < Gi'Gj>CGi+j (7) Obviously any superalgebra is Z 2 graded because of Eqs. (I) and (3) we have < Si,S j …
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