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Showing 1 to 12 of 12 for “"Superalgebras"”.
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Quantum Toroidal Superalgebras
… E(s) is defined. To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed. The superalgebra E(s) contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂(m|n) with parity "s", called vertical and …
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Superalgebras with superinvolution
… of this thesis is to present in the setting of superalgebras with superinvolution some of the most interesting and challenging problems of combinatorial PI-theory (the theory of polynomial identities), which have already been addressed in the field of associative algebras or of algebras with …
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Modular invariance for vertex operator superalgebras
… (VOAs) to the setting of vertex operator superalgebras (VOSAs) with rational, rather than integer, conformal weights. To recover SL₂ (Z)-invariance, it turns out to be necessary to consider characters of twisted modules. Initially we assume our VOSA to be rational, then we replace …
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Representations of vertex operator algebras and superalgebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1995.
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Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
… $\cC l_{p,q}$. In the second part we consider superalgebras of Krichever-Novikov (K-N) type. Krichever and Novikov introduced a family of Lie algebras with two marked points generalizing the Witt algebra and its central extension called the Virasoro algebra. The K-N Lie (super)algebras for more …
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Supersymmetric Schur functions and Lie superalgebra representations
Lie superalgebras and their representations continue to play an important role in the understanding and exploitation of supersymmetry in physical systems. The Lie superalgebras that we consider, namely gl(m|n) and sl(m|n) (sometimes denoted as U(m|n) and SU(m|n)), have applications in quantum …
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Spherical Functions on Supersymmetric Spaces and Calogero-Moser-Sutherland Operators
… Hopf superalgebra structure of enveloping superalgebras. We present a comprehensive framework for spherical functions within the context of symmetric pairs (𝔤, 𝔨) of Lie superalgebras. Our analysis begins by constructing an algebraic radial component map for the spherical functions. …
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On Lie Theory in the Verlinde Category
… can be used to provide new constructions of Lie superalgebras, and in particular exceptional simple Lie superalgebras in low characteristic. We also show that in characteristic 5 a new algebraic structure we call a "weak Jordan algebra" arises. Finally, we classify bilinear forms in the Verlinde …
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Frobenius Brauer Categories
… information on super-mathematics and Frobenius superalgebras needed to understand the new results.
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Odd symmetric functions and categorification
We introduce q- and signed analogues of several constructions in and around the theory of symmetric functions. The most basic of these is the Hopf superalgebra of odd symmetric functions. This algebra is neither (super-)commutative nor (super-)cocommutative, yet its combinatorics still exhibit many …