Displaying similar documents to “How to categorify one-half of quantum 𝔤𝔩(1|2)”

Quantum sections and Gauge algebras.

Lieven Le Bruyn, Freddy van Oystaeyen (1992)

Publicacions Matemàtiques

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Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties...

Quantum deformation of relativistic supersymmetry

Sobczyk, Jan

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From the text: The author reviews recent research on quantum deformations of the Poincaré supergroup and superalgebra. It is based on a series of papers (coauthored by P. Kosiński, J. Lukierski, P. Maślanka and A. Nowicki) and is motivated by both mathematics and physics. On the mathematical side, some new examples of noncommutative and noncocommutative Hopf superalgebras have been discovered. Moreover, it turns out that they have an interesting internal structure of graded bicrossproduct....

Chaotic decompositions in ℤ 2 -graded quantum stochastic calculus

Timothy Eyre (1998)

Banach Center Publications

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A brief introduction to ℤ 2 -graded quantum stochastic calculus is given. By inducing a superalgebraic structure on the space of iterated integrals and using the heuristic classical relation df(Λ) = f(Λ + dΛ) - f(Λ) we provide an explicit formula for chaotic expansions of polynomials of the integrator processes of ℤ 2 -graded quantum stochastic calculus.

The ℤ₂-graded sticky shuffle product Hopf algebra

Robin L. Hudson (2006)

Banach Center Publications

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By abstracting the multiplication rule for ℤ₂-graded quantum stochastic integrals, we construct a ℤ₂-graded version of the Itô Hopf algebra, based on the space of tensors over a ℤ₂-graded associative algebra. Grouplike elements of the corresponding algebra of formal power series are characterised.

Induced modules of strongly group-graded algebras

Th. Theohari-Apostolidi, H. Vavatsoulas (2007)

Colloquium Mathematicae

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Various results on the induced representations of group rings are extended to modules over strongly group-graded rings. In particular, a proof of the graded version of Mackey's theorem is given.

ℤ -graded Lie superalgebras of infinite depth and finite growth

Nicoletta Cantarini (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In 1998 Victor Kac classified infinite-dimensional ℤ -graded Lie superalgebras of finite depth. We construct new examples of infinite-dimensional Lie superalgebras with a ℤ -gradation of infinite depth and finite growth and classify ℤ -graded Lie superalgebras of infinite depth and finite growth under suitable hypotheses.