Results 21 to 30 of about 12,045 (118)
C⁎‐Basic Construction from the Conditional Expectation on the Drinfeld Double
Journal of Function Spaces, Volume 2019, Issue 1, 2019., 2019 Let D(G) be the Drinfeld double of a finite group G and D(G; H) be the crossed product of C(G) and CH, where H is a subgroup of G. Then the sets D(G) and D(G; H) can be made C⁎‐algebras naturally. Considering the C⁎‐basic construction C⁎〈D(G), e〉 from the conditional expectation E of D(G) onto D(G; H), one can construct a crossed product C⁎‐algebra C(G/
Qiaoling Xin +3 more
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New Braided T‐Categories over Weak Crossed Hopf Group Coalgebras
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 Let H be a weak crossed Hopf group coalgebra over group π; we first introduce a kind of new α‐Yetter‐Drinfel’d module categories 𝒲𝒴𝒟α(H) for α ∈ π and use it to construct a braided T‐category 𝒲𝒴𝒟(H). As an application, we give the concept of a Long dimodule category H𝒲ℒH for a weak crossed Hopf group coalgebra H with quasitriangular and ...
Xuan Zhou, Tao Yang, Jaan Janno
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Microscopic Description of 2D Topological Phases, Duality, and 3D State Sums
Advances in Mathematical Physics, Volume 2010, Issue 1, 2010., 2010 Doubled topological phases introduced by Kitaev, Levin, and Wen supported on two‐dimensional lattices are Hamiltonian versions of three‐dimensional topological quantum field theories described by the Turaev‐Viro state sum models. We introduce the latter with an emphasis on obtaining them from theories in the continuum.
Zoltán Kádár +3 more
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Some details of proofs of theorems related to the quantum dynamical Yang‐Baxter equation
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 12, Page 793-806, 2000., 2000 This paper of tutorial nature gives some further details of proofs of some theorems related to the quantum dynamical Yang‐Baxter equation. This mainly expands proofs given in “Lectures on the dynamical Yang‐Baxter equation” by Etingof and Schiffmann, math.QA/9908064.
Tom H. Koornwinder
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Local quasitriangular Hopf algebras. [PDF]
, 2006 We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite
Shouchuan Zhang, M. Gould, Yao-Z Zhang
semanticscholar +1 more source
On quiver-theoretic description for quasitriangularity of Hopf algebras
Journal of Algebra, 2010 19 ...
Huang, Hua-Lin, Liu, Gongxiang
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HOMOLOGICAL DIMENSION OF SMASH PRODUCT OVER QUASITRIANGULAR WEAK HOPF ALGEBRA
, 2015 Let (H,R) be a quasitriangular weak Hopf algebra, and A a quantum commutative weak H-module algebra. We establish the relationship of homological dimensions between weak smash product algebra A#H and A under some conditions.
Zhong-wei Wang
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Minimal Quasitriangular Hopf Algebras
Journal of Algebra, 1993 A quasitriangular Hopf algebra is minimal if it has no quasitriangular sub-Hopf algebra. The Drinfeld double \(D(H)\) of a finite-dimensional Hopf algebra \(H\) is minimal. The author shows that every minimal quasitriangular Hopf algebra is finite-dimensional, and is the quotient of a \(D(H)\).
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QUASITRIANGULAR HOPF ALGEBRAS, BRAID GROUPS AND QUANTUM ENTANGLEMENT [PDF]
International Journal of Quantum Information, 2013 The aim of the paper is to provide a method to obtain representations of the braid group through a set of quasitriangular Hopf algebras. In particular, these algebras may be derived from group algebras of cyclic groups with additional algebraic structures.
Pinto, Eric +2 more
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Braided Hopf algebras and gauge transformations II: $*$-structures and examples
, 2022 We consider noncommutative principal bundles which are equivariant under a triangular Hopf algebra. We present explicit examples of infinite dimensional braided Lie and Hopf algebras of infinitesimal gauge transformations of bundles on noncommutative ...
Landi, Giovanni +5 more
core +1 more source