By N. Andruskiewitsch, I. Angiono (auth.), Chengming Bai, Jürgen Fuchs, Yi-Zhi Huang, Liang Kong, Ingo Runkel, Christoph Schweigert (eds.)
ISBN-10: 3642393829
ISBN-13: 9783642393822
ISBN-10: 3642393837
ISBN-13: 9783642393839
The current quantity is a suite of 7 papers which are both
based at the talks offered on the workshop "Conformal box theories and tensor different types" held June thirteen to June 17, 2011 at the
Beijing foreign middle for Mathematical examine, Peking collage, or are extensions of the fabric provided within the talks on the workshop. those papers current new advancements past
rational conformal box theories and modular tensor different types and new functions in arithmetic and physics. the themes lined contain tensor different types from illustration different types of Hopf algebras, purposes of conformal box theories and tensor different types to topological stages and gapped structures, logarithmic conformal box theories and the corresponding non-semisimple tensor different types, and new advancements within the illustration idea of vertex operator algebras. a few of the papers comprise specific introductory fabric that's necessary for graduate scholars and researchers trying to find an creation to those learn instructions. The papers additionally speak about intriguing fresh advancements within the zone of conformal box theories, tensor different types and their purposes and may be super helpful for researchers operating in those areas.
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Adv. Math. 143, 357–375 (1999) 21. : Cosovereign Hopf algebras. J. Pure Appl. Algebra 157, 121–133 (2001) 22. : Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors. Lect. Notes Math. 832, 103–169 (1980) 23. : Finite dimensional algebras and highest weight categories. J. Reine Angew. Math. 391, 85–99 (1988) 24. : Characters and a Verlinde-type formula for symmetric Hopf algebras. J. Algebra 320, 4300–4316 (2008) 25. : Structure constants related to symmetric Hopf algebras. J. Algebra 324, 3219–3240 (2010) 26.
Consider the morphisms of algebras ρV : B(V ) → u, ρW : B(W ) → u and ρΓ : kΓ → u, given by ρV (vi ) = vi , ρW (wi ) = wi , ρΓ (gi ) = gi , i ∈ I. Then (a) ρV , ρW , ρΓ give rise to isomorphisms B(W ) u− , B(V )#kΓ ub . (b) The map B(V ) ⊗ B(W ) ⊗ kΓ → u, v ⊗ w ⊗ g → ρV (v)ρW (w)ρΓ (g) is a coalgebra isomorphism. (c) The multiplication maps u− ⊗ ub → u, ub ⊗ u− → u are linear isomorphisms. 26 N. Andruskiewitsch et al. 8 in [11]. Now suppose that one would like to define tilting modules over u, ignoring that this is not a quasi-hereditary algebra.
Given i ∈ I, we define the i-th reflection of (V , c). Define si ∈ Aut Λ 28 N. Andruskiewitsch et al. 12). Then si (V , c) = (V , c ), where C is the braiding of diagonal type with matrix (qrs )r,s∈I . Here qrs = (si (αr )|si (αs )); we omit the mention to the braidings c, c , etc. 12 in [42]). 26 in [15]), compatible with those of u(V ). There is a Λ-grading on T (W ⊕ V )#kQ given by deg γ = 0, γ ∈ Q, deg vi = αi = − deg wi , i ∈ I; it extends to gradings of u(V ) and U(V ). Hence we may consider categories CU and so on.
Conformal Field Theories and Tensor Categories: Proceedings of a Workshop Held at Beijing International Center for Mathematical Research by N. Andruskiewitsch, I. Angiono (auth.), Chengming Bai, Jürgen Fuchs, Yi-Zhi Huang, Liang Kong, Ingo Runkel, Christoph Schweigert (eds.)
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