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Gorenstein subrings of invariants under Hopf algebra actions
Journal of Algebra, 2009 Ellen Kirkman, J Kuzmanovich
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Kitaev Lattice Models as a Hopf Algebra Gauge Theory
, 2016We prove that Kitaev’s lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to the combinatorial quantisation of Chern–Simons theory for the Drinfeld double D(H). This shows that Kitaev models are a special case of the older and
C. Meusburger
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, 1999
:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann–Hilbert ...
A. Connes, D. Kreimer
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:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann–Hilbert ...
A. Connes, D. Kreimer
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Hopf algebras over hopf algebras
Annali di Matematica Pura ed Applicata, 1967In any category with products and a terminal object one may define the notions of group, module over a group etc. if f: R′→R is a homomorphism of groups, and M an R-module, then one has an induced R′-module f*(M). If one is working in the category of sets, one may define a functor left adjoint to f* by N→R⊗R′ N, where N is an R′-module.
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The Hopf algebra of Möbius intervals
Theory and Applications of Categories, 2010An unpublished result by the first author states that there exists a Hopf algebra H such that for any Möbius category C (in the sense of Leroux) there exists a canonical algebra morphism from the dual H∗ of H to the incidence algebra of C.
F. Lawvere, M. Menni
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Journal of the London Mathematical Society, 1991
This paper deals with graded Hopf algebras of the kind represented by the homology of the loops on simply connected spaces of finite type or universal enveloping algebras of graded Lie algebras of finite type (i.e. degree-wise finite-dimensional). In particular, finitely generated nilpotent (elliptic) Hopf algebras are characterized in several ways: by
Félix, Yves +2 more
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This paper deals with graded Hopf algebras of the kind represented by the homology of the loops on simply connected spaces of finite type or universal enveloping algebras of graded Lie algebras of finite type (i.e. degree-wise finite-dimensional). In particular, finitely generated nilpotent (elliptic) Hopf algebras are characterized in several ways: by
Félix, Yves +2 more
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Nonlinear Evolution Equations and Dynamical Systems, 2003
Abstract: This lecture was given in UIA at Antwerp, and in USTC at Hefei, aiming at outlining a construction of non-commutative, non-cocommutative pointed Hopf algebras via quivers, given by Cibils and Rosso(3). We thank Sen Hu for his interest to include it in this proceeding. To save the space, we omit details here.
Van Oystaeyen, F., Zhang, P.
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Abstract: This lecture was given in UIA at Antwerp, and in USTC at Hefei, aiming at outlining a construction of non-commutative, non-cocommutative pointed Hopf algebras via quivers, given by Cibils and Rosso(3). We thank Sen Hu for his interest to include it in this proceeding. To save the space, we omit details here.
Van Oystaeyen, F., Zhang, P.
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Canadian Journal of Mathematics, 1967
A coalgebra over the field F is a vector space A over F, with maps δ: A → A ⊗ A and ∊: A → F such that1and2The notion of coalgebra is dual to the notion of algebra with unit, with δ as coproduct (equation (1) says that δ is associative) and ∊ as the unit map (equation (2) is just the statement that ∊ is a unit for the coproduct δ).
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A coalgebra over the field F is a vector space A over F, with maps δ: A → A ⊗ A and ∊: A → F such that1and2The notion of coalgebra is dual to the notion of algebra with unit, with δ as coproduct (equation (1) says that δ is associative) and ∊ as the unit map (equation (2) is just the statement that ∊ is a unit for the coproduct δ).
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American Journal of Mathematics, 1977
Let A be a finite dimensional Hopf algebra with antipode s over a field k. In (6) the structure of s and s2 is seen to be closely related to the important algebraic features of A and A*. This paper furthers the investigation. More generally "locally finite" bialgebra endomorphisms t:A ->A of an arbitrary Hopf algebra A are considered (this means A is ...
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Let A be a finite dimensional Hopf algebra with antipode s over a field k. In (6) the structure of s and s2 is seen to be closely related to the important algebraic features of A and A*. This paper furthers the investigation. More generally "locally finite" bialgebra endomorphisms t:A ->A of an arbitrary Hopf algebra A are considered (this means A is ...
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Hopf Algebra Extensions of Group Algebras and Tambara-Yamagami Categories
, 2008We determine the structure of Hopf algebras that admit an extension of a group algebra by the cyclic group of order 2. We study the corepresentation theory of such Hopf algebras, which provide a generalization, at the Hopf algebra level, of the so called
S. Natale
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