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36 relations: *-algebra, Annals of Mathematics, Antilinear map, Anyonic Lie algebra, Boson, BRST quantization, Cambridge University Press, Category theory, Commutative ring, Equivariant map, Exterior algebra, Fermion, Gerstenhaber algebra, Graded Lie algebra, Graded ring, Graduate Studies in Mathematics, Hopf algebra, Indagationes Mathematicae, Involution (mathematics), Lie algebra, Lie algebra representation, Linear map, Mathematics, Representation of a Lie superalgebra, ScienceDirect, Superalgebra, Supergravity, Supergroup (physics), Superspace, Superstring theory, Supersymmetry, Symmetry, Theoretical physics, Universal enveloping algebra, Victor Kac, Whitehead product.
*-algebra
In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings and, where is commutative and has the structure of an associative algebra over.
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Annals of Mathematics
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.
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Antilinear map
In mathematics, a mapping f:V\to W from a complex vector space to another is said to be antilinear (or conjugate-linear) if for all a, \, b \, \in \mathbb and all x, \, y \, \in V, where \bar and \bar are the complex conjugates of a and b respectively.
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Anyonic Lie algebra
In mathematics, an anyonic Lie algebra is a U(1) graded vector space L over \mathbb equipped with a bilinear operator and linear maps \varepsilon\colon L\to\mathbb and \Delta\colon L \to L\otimes L satisfying for pure graded elements X, Y, and Z.
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Boson
In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics.
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BRST quantization
In theoretical physics, the BRST formalism, or BRST quantization (where the BRST refers to Becchi, Rouet, Stora and Tyutin) denotes a relatively rigorous mathematical approach to quantizing a field theory with a gauge symmetry.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Category theory
Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).
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Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
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Equivariant map
In mathematics, equivariance is a form of symmetry for functions from one symmetric space to another.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.
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Gerstenhaber algebra
In mathematics and theoretical physics, a Gerstenhaber algebra (sometimes called an antibracket algebra or braid algebra) is an algebraic structure discovered by Murray Gerstenhaber (1963) that combines the structures of a supercommutative ring and a graded Lie superalgebra.
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Graded Lie algebra
In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket.
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Graded ring
In mathematics, in particular abstract algebra, a graded ring is a ring that is a direct sum of abelian groups R_i such that R_i R_j \subseteq R_.
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Graduate Studies in Mathematics
Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS).
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Hopf algebra
In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property.
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Indagationes Mathematicae
Indagationes Mathematicae (from Latin: inquiry, search, investigation of the mathematics) is a Netherlands mathematics journal.
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Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
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Lie algebra
In mathematics, a Lie algebra (pronounced "Lee") is a vector space \mathfrak g together with a non-associative, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g; (x, y) \mapsto, called the Lie bracket, satisfying the Jacobi identity.
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Lie algebra representation
In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator.
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Linear map
In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Representation of a Lie superalgebra
In the mathematical field of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a '''Z'''2-graded vector space V, such that if A and B are any two pure elements of L and X and Y are any two pure elements of V, then Equivalently, a representation of L is a Z2-graded representation of the universal enveloping algebra of L which respects the third equation above.
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ScienceDirect
ScienceDirect is a website which provides subscription-based access to a large database of scientific and medical research.
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Superalgebra
In mathematics and theoretical physics, a superalgebra is a Z2-graded algebra.
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Supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity where supersymmetry obeys locality; in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model.
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Supergroup (physics)
The concept of supergroup is a generalization of that of group.
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Superspace
Superspace is the coordinate space of a theory exhibiting supersymmetry.
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Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings.
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Supersymmetry
In particle physics, supersymmetry (SUSY) is a theory that proposes a relationship between two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin.
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
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Universal enveloping algebra
In mathematics, a universal enveloping algebra is the most general (unital, associative) algebra that contains all representations of a Lie algebra.
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Victor Kac
Victor Gershevich (Grigorievich) Kac (Виктор Гершевич (Григорьевич) Кац; born 19 December 1943 in Buguruslan, Russia, USSR) is a Soviet and American mathematician at MIT, known for his work in representation theory.
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Whitehead product
In mathematics, the Whitehead product is a graded quasi-Lie algebra structure on the homotopy groups of a space.
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Lie Superalgebras, Lie superalgebras, Lie superbracket, Star Lie superalgebra, Super Jacobi identity, Super Lie algebra, SuperJacobi identity, Supercommutator, Superjacobi identity.
References
[1] https://en.wikipedia.org/wiki/Lie_superalgebra
