Results 1 to 10 of about 12,448 (96)
The category of affine algebraic regular monoids
AIMS Mathematics, 2022 The main aim of this study is to characterize affine weak $ k $-algebra $ H $ whose affine $ k $-variety $ S = M_{k}(H, k) $ admits a regular monoid structure.
Haijun Cao, Fang Xiao
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Rota–Baxter Operators on Cocommutative Weak Hopf Algebras
Mathematics, 2021 In this paper, we first introduce the concept of a Rota–Baxter operator on a cocommutative weak Hopf algebra H and give some examples. We then construct Rota–Baxter operators from the normalized integral, antipode, and target map of H.
Zhongwei Wang +3 more
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Automorphism groups of representation rings of the weak Sweedler Hopf algebras
AIMS Mathematics, 2022 Let $ \mathfrak{w}^{s}_{2, 2}(s = 0, 1) $ be two classes of weak Hopf algebras corresponding to the Sweedler Hopf algebra, and $ r(\mathfrak{w}^{s}_{2, 2}) $ be the representation rings of $ \mathfrak{w}^{s}_{2, 2} $.
Dong Su , Shilin Yang
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Brick polytopes, lattices and Hopf algebras [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Generalizing the connection between the classes of the sylvester congruence and the binary trees, we show that the classes of the congruence of the weak order on Sn defined as the transitive closure of the rewriting rule UacV1b1 ···VkbkW ≡k UcaV1b1 ...
Vincent Pilaud
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On lattice models of gapped phases with fusion category symmetries
Journal of High Energy Physics, 2022 We construct topological quantum field theories (TQFTs) and commuting projector Hamiltonians for any 1+1d gapped phases with non-anomalous fusion category symmetries, i.e. finite symmetries that admit SPT phases.
Kansei Inamura
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Double Weak Hopf Quiver and Its Path Coalgebra
Journal of Function Spaces, 2022 The main input of this research is the introduction of the concept of double weak Hopf quiver (DWHQ). In addition, the structures of weak Hopf algebra (WHA) are obtained through path coalgebra of the proposed quivers. Furthermore, the module and comodule
Muhammad Naseer Khan +5 more
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Fermionization of fusion category symmetries in 1+1 dimensions
Journal of High Energy Physics, 2023 We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation category Rep(H) of a semisimple weak Hopf algebra H, the ...
Kansei Inamura
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Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras [PDF]
, 2004 The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations ...
Aizawa N. +6 more
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International Journal of Mathematics and Mathematical Sciences, 2010 We introduce a class of noncommutative and noncocommutative weak Hopf algebras with infinite Ext quivers and study their structure. We decompose them into a direct sum of two algebras. The coalgebra structures of these weak Hopf algebras are described by
Dongming Cheng
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On bialgebras associated with paths and essential paths on ADE graphs [PDF]
, 2004 We define a graded multiplication on the vector space of essential paths on a graph $G$ (a tree) and show that it is associative. In most interesting applications, this tree is an ADE Dynkin diagram. The vector space of length preserving endomorphisms of
Coquereaux, Robert, Garcia, Ariel O.
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