Results 1  10
of
18
Braided Hopf algebras over non abelian finite groups
 Acad. Nac. Ciencias (Córdoba
"... Abstract. In the last years a new theory of Hopf algebras has begun to be developed: that of Hopf algebras in braided categories, or, briefly, braided Hopf algebras. This is a survey of general aspects of the theory with emphasis in H HYD, the Yetter–Drinfeld category over H, where H is the group al ..."
Abstract

Cited by 40 (11 self)
 Add to MetaCart
Abstract. In the last years a new theory of Hopf algebras has begun to be developed: that of Hopf algebras in braided categories, or, briefly, braided Hopf algebras. This is a survey of general aspects of the theory with emphasis in H HYD, the Yetter–Drinfeld category over H, where H is the group algebra of a non abelian finite group Γ. We discuss a special class of braided graded Hopf algebras from different points of view following Lusztig, Nichols and Schauenburg. We present some finite dimensional examples arising in an unpublished work by Milinski and Schneider. Sinopsis. En los últimos años comenzó a ser desarrollada una nueva teoría de álgebras de Hopf en categorías trenzadas, o brevemente, álgebras de Hopf trenzadas. Presentamos aquí aspectos generales de la teoría con énfasis en H HYD, la categoría de Yetter–Drinfeld sobre H, donde H es el álgebra de grupo de un grupo finito no abeliano Γ. Discutimos una clase especial de álgebras de Hopf trenzadas graduadas desde diferentes puntos de vista, siguiendo a Lusztig, Nichols y Schauenburg. Presentamos algunos ejemplos de dimensión finita que aparecen en un trabajo inédito de Milinski y Schneider. 0. Introduction and notations 0.1. Introduction.
Duality theorem and Drinfeld double in braided tensor categories, Algebra colloq
"... Let H be a finite Hopf algebra with CH,H = C −1 H,H. The duality theorem is shown for H, i.e., (R#H)#H ˆ ∗ ∼ = R ⊗ (H ¯⊗H ˆ ∗ ) as algebras in C. Also, it is proved that the Drinfeld double (D(H),[b]) is a quasitriangular Hopf algebra in C. ..."
Abstract

Cited by 8 (7 self)
 Add to MetaCart
Let H be a finite Hopf algebra with CH,H = C −1 H,H. The duality theorem is shown for H, i.e., (R#H)#H ˆ ∗ ∼ = R ⊗ (H ¯⊗H ˆ ∗ ) as algebras in C. Also, it is proved that the Drinfeld double (D(H),[b]) is a quasitriangular Hopf algebra in C.
YetterDrinfeld categories for quasiHopf algebras
 Comm. Algebra
"... Abstract. We show that all possible categories of YetterDrinfeld modules over a quasiHopf algebra H are isomorphic. We prove also that the category H H YDfd of finite dimensional left YetterDrinfeld modules is rigid and then we compute explicitly the canonical isomorphisms in H H YDfd. Finally, w ..."
Abstract

Cited by 7 (7 self)
 Add to MetaCart
Abstract. We show that all possible categories of YetterDrinfeld modules over a quasiHopf algebra H are isomorphic. We prove also that the category H H YDfd of finite dimensional left YetterDrinfeld modules is rigid and then we compute explicitly the canonical isomorphisms in H H YDfd. Finally, we show that certain duals of H0, the braided Hopf algebra introduced in [6, 7], are isomorphic as braided Hopf algebras if H is a finite dimensional triangular quasiHopf algebra.
A categorical approach to Turaev’s Hopf groupcoalgebras
 Commun. Algebra
, 2006
"... Abstract. We show that Turaev’s groupcoalgebras and Hopf groupcoalgebras ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract. We show that Turaev’s groupcoalgebras and Hopf groupcoalgebras
Lagrange’s theorem for Hopf monoids in species
, 2012
"... Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras, ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
Abstract. Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras,
FURTHER RESULTS ON COSET REPRESENTATIVE CATEGORIES
, 2008
"... This paper is devoted to further results on the nontrivially associated categories C and D, which are constructed from a choice of coset representatives for a subgroup of a finite group. We look at the construction of integrals in the algebras A and D in the categories. These integrals are used to c ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
This paper is devoted to further results on the nontrivially associated categories C and D, which are constructed from a choice of coset representatives for a subgroup of a finite group. We look at the construction of integrals in the algebras A and D in the categories. These integrals are used to construct abstract projection operators to show that general objects in D can be split into a sum of simple objects. The braided Hopf algebra D is shown to be braided cocommutative, but not braided commutative. Extensions of the categories and their connections with conjugations and inner products are discussed.
More properties of YetterDrinfeld modules over quasiHopf algebras, in ”Hopf algebras in noncommutative geometry and
 Lecture Notes Pure Appl. Math. 239
, 2004
"... Abstract. We generalize various properties of YetterDrinfeld modules over Hopf algebras to quasiHopf algebras. The dual of a finite dimensional YetterDrinfeld module is again a YetterDrinfeld module. The algebra H0 in the category of YetterDrinfeld modules that can be obtained by modifying the ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. We generalize various properties of YetterDrinfeld modules over Hopf algebras to quasiHopf algebras. The dual of a finite dimensional YetterDrinfeld module is again a YetterDrinfeld module. The algebra H0 in the category of YetterDrinfeld modules that can be obtained by modifying the multiplication in a proper way is quantum commutative. We give a Structure
A quantum double construction in Rel
, 2010
"... We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of ..."
Abstract
 Add to MetaCart
We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of
Braided mLie Algebras
, 2004
"... Braided mLie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided mLie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided mLie algebra ..."
Abstract
 Add to MetaCart
Braided mLie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided mLie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided mLie algebras are given, which are generalized matrix braided mLie algebras and braided mLie subalgebras of EndFM, where M is a YetterDrinfeld module over B with dim B < ∞. In particular, generalized classical braided mLie algebras slq,f(GMG(A),F) and ospq,t(GMG(A),M,F) of generalized matrix algebra GMG(A) are constructed and their connection with special generalized matrix Lie superalgebra sls,f(GMZ2 (As),F) and orthosymplectic generalized matrix Lie super algebra osps,t(GMZ2 (As),M s,F) are established. The relationship between representations of braided mLie algebras and their associated algebras are established. 0
The factorization of braided Hopf algebras and braided version of the 8th Kaplansky’s conjecture
, 2006
"... We obtain the double factorization of braided bialgebras or braided Hopf algebras, give relation among integrals and semisimplicity of braided Hopf algebra and its factors. We find an example which show that the 8th Kaplansky’s conjecture does not hold for braided Hopf algebras. ..."
Abstract
 Add to MetaCart
We obtain the double factorization of braided bialgebras or braided Hopf algebras, give relation among integrals and semisimplicity of braided Hopf algebra and its factors. We find an example which show that the 8th Kaplansky’s conjecture does not hold for braided Hopf algebras.