317,783 research outputs found
Twin TQFTs and Frobenius algebras
We introduce the category of singular 2-dimensional cobordisms and show that
it admits a completely algebraic description as the free symmetric monoidal
category on a twin Frobenius algebra, by providing a description of this
category in terms of generators and relations. A twin Frobenius algebra (C, W,
z, z^*) consists of a commutative Frobenius algebra C, a symmetric Frobenius
algebra W, and an algebra homomorphism z: C - > W with dual z^*: W -> C,
satisfying some extra conditions. We also introduce a generalized 2-dimensional
Topological Quantum Field Theory defined on singular 2-dimensional cobordisms
and show that it is equivalent to a twin Frobenius algebra in a symmetric
monoidal category.Comment: 38 pages, many figures; some concepts have been clarified; references
and proofs have been adde
Solvable Leibniz Algebras with Filiform Nilradical
In this paper we continue the description of solvable Leibniz algebras whose nilradical
is a filiform algebra. In fact, solvable Leibniz algebras whose nilradical is a naturally graded filiform
Leibniz algebra are described in [6] and [8]. Here we extend the description to solvable Leibniz algebras
whose nilradical is a filiform algebra. We establish that solvable Leibniz algebras with filiform Lie
nilradical are Lie algebras.Ministerio de EconomÃa y Competitividad MTM2013-43687-
A Littlewood-Richardson rule for evaluation representations of quantum affine sl(n)
We give a combinatorial description of the composition factors of the
induction product of two evaluation modules of the affine Iwahori-Hecke algebra
of type GL(m). Using quantum affine Schur-Weyl duality, this yields a
combinatorial description of the composition factors of the tensor product of
two evaluation modules of the quantum affine algebra of type sl(n)
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