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pro vyhledávání: '"Kirillov Jr., Alexander A."'
Publikováno v:
Quantum Topology 13 (2022), no. 1, pp. 1-54
In [BK], it is shown that the Turaev-Viro invariants defined for a spherical fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with corners. In [Kir], an equivalent formulation for the 2-1 part of the theory (2-manifolds with boundar
Externí odkaz:
http://arxiv.org/abs/2002.08571
Let $V$ be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the notions o
Externí odkaz:
http://arxiv.org/abs/1406.3420
Autor:
Kirillov Jr, Alexander, Thind, Jaimal
In this paper, using the quantum McKay correspondence, we construct the "derived category" of G-equivariant sheaves on the quantum projective line at a root of unity. More precisely, we use the representation theory of U_{q}sl(2) at root of unity to
Externí odkaz:
http://arxiv.org/abs/1210.4565
In this paper, we examine Kitaev's lattice model for an arbitrary complex, semisimple Hopf algebra. We prove that this model gives the same topological invariants as Turaev-Viro theory. Using the description of Turaev-Viro theory as an extended TQFT,
Externí odkaz:
http://arxiv.org/abs/1206.2308
Autor:
Kirillov Jr, Alexander
In this paper, we describe the relation between the Turaev--Viro TQFT and the string-net space introduced in the papers of Levin and Wen. In particular, the case of surfaces with boundary is considered in detail.
Comment: 27 pages, LaTeX with Ti
Comment: 27 pages, LaTeX with Ti
Externí odkaz:
http://arxiv.org/abs/1106.6033
Autor:
Kirillov Jr, Alexander
Publikováno v:
Algebr. Geom. Topol. 12 (2012) 95-108
In this note, we introduce a class of cell decompositions of PL manifolds and polyhedra which are more general than triangulations yet not as general as CW complexes; we propose calling them PLCW complexes. The main result is an analog of Alexander's
Externí odkaz:
http://arxiv.org/abs/1009.4227
Autor:
Kirillov Jr, Alexander, Thind, Jaimal
Let \Gamma be a Dynkin diagram of type A,D,E and let R denote the corresponding root system. In this paper we give a categorical construction of R from \Gamma. Instead of choosing an orientation of \Gamma and studying representations of the associate
Externí odkaz:
http://arxiv.org/abs/1007.2623
In this paper we show how one can extend Turaev-Viro invariants, defined for an arbitrary spherical fusion category $C$, to 3-manifolds with corners. We demonstrate that this gives an extended TQFT which conjecturally coincides with the Reshetikhin-T
Externí odkaz:
http://arxiv.org/abs/1004.1533
Autor:
Kirillov Jr., Alexander, Thind, Jaimal
Let g be a Lie algebra of type A,D,E with fixed Cartan subalgebra h, root system R and Weyl group W. We show that a choice of Coxeter element C gives a root basis for g. Moreover we show that this root basis gives a purely combinatorial construction
Externí odkaz:
http://arxiv.org/abs/0811.2324
Autor:
Kirillov Jr, Alexander, Prince, Tanvir
In this paper, we extend the notion of modular functor and fusion category to what we called $G$ equivariant modular functor and $G$ equivariant fusion category, where $G$ is a finite group, and establish a correspondence between between these notion
Externí odkaz:
http://arxiv.org/abs/0807.0939