Alexei Davydov
Commutative Algebras in Fibonacci Categories.
Mon, 03/21/2011 - 16:01 — SomNambulAuthors: Alexei Davydov, Tom Booker
Subjects: Category Theory
AbstractBy studying NIM-representations we show that the Fibonacci category and its
tensor powers are completely anisotropic; that is, they do not have any
non-trivial separable commutative ribbon algebras. As an application we deduce
that a chiral algebra with the representation category equivalent to a product
of Fibonacci categories is maximal; that is, it is not a proper subalgebra of
another chiral algebra. In particular the chiral algebras of the Yang-Lee
model, the WZW models of G2 and F4 at level 1, as well as their tensor powers,
are maximal.The Witt group of non-degenerate braided fusion categories.
Tue, 09/14/2010 - 15:01 — SomNambulAuthors: Michael Mueger, Dmitri Nikshych, Victor Ostrik, Alexei Davydov
Subjects: Quantum Algebra
AbstractWe give a characterization of Drinfeld centers of fusion categories as
non-degenerate braided fusion categories containing a Lagrangian algebra.
Further we study the quotient of the monoid of non-degenerate braided fusion
categories modulo the submonoid of the Drinfeld centers and show that its
formal properties are similar to those of the classical Witt group.Full centre of an H -module algebra.
Tue, 02/02/2010 - 16:01 — SomNambulAuthors: Alexei Davydov
Subjects: Rings and Algebras
AbstractWe apply the full centre construction, defined in arXiv:0908.1250, to
algebras in and module categories over categories of representations of Hopf
algebras. We obtain a compact formula for the full centre of a module algebra
over a Hopf algebra.
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