scholarly journals Tensor Products and Support Varieties for Some Noncocommutative Hopf Algebras

2017 ◽  
Vol 21 (2) ◽  
pp. 259-276 ◽  
Author(s):  
Julia Yael Plavnik ◽  
Sarah Witherspoon
Keyword(s):  
Hopf Algebras ◽  
Tensor Products ◽  
Support Varieties

scholarly journals Examples of support varieties for Hopf algebras with noncommutative tensor products

2014 ◽  
Vol 102 (6) ◽  
pp. 513-520 ◽  
Author(s):  
Dave Benson ◽  
Sarah Witherspoon
Keyword(s):  
Hopf Algebras ◽  
Tensor Products ◽  
Support Varieties

scholarly journals On support varieties and tensor products for finite dimensional algebras

2020 ◽  
Vol 547 ◽  
pp. 226-237
Author(s):  
Petter Andreas Bergh ◽  
Mads Hustad Sandøy ◽  
Øyvind Solberg
Keyword(s):  
Tensor Products ◽  
Finite Dimensional ◽  
Support Varieties ◽  
Finite Dimensional Algebras

(𝜃,ω)-Twisted Radford’s Hom-biproduct and ϖ-Yetter–Drinfeld modules for Hom-Hopf algebras

2020 ◽  
Vol 19 (03) ◽  
pp. 2050046
Author(s):  
Xiao-Li Fang ◽  
Tae-Hwa Kim
Keyword(s):  
Hopf Algebras ◽  
Sufficient Conditions ◽  
Tensor Products ◽  
Product Formula ◽  
Necessary And Sufficient Conditions ◽  
Drinfeld Modules ◽  
Associative Algebras ◽  
Necessary And Sufficient

To unify different definitions of smash Hom-products in a Hom-bialgebra [Formula: see text], we firstly introduce the notion of [Formula: see text]-twisted smash Hom-product [Formula: see text]. Secondly, we find necessary and sufficient conditions for the twisted smash Hom-product [Formula: see text] and the twisted smash Hom-coproduct [Formula: see text] to afford a Hom-bialgebra, which generalize the well-known Radford’s biproduct and the Hom-biproduct obtained in [H. Li and T. Ma, A construction of the Hom-Yetter–Drinfeld category, Colloq. Math. 137 (2014) 43–65]. Furthermore, we introduce the notion of the category of [Formula: see text]-Yetter-Drinfeld modules which unifies the ones of Hom-Yetter Drinfeld category appeared in [H. Li and T. Ma, A construction of the Hom-Yetter–Drinfeld category, Colloq. Math. 137 (2014) 43–65] and [A. Makhlouf and F. Panaite, Twisting operators, twisted tensor products and smash products for Hom-associative algebras, J. Math. Glasgow 513–538 (2016) 58]. Finally, we prove that the [Formula: see text]-twisted Radford’s Hom-biproduct [Formula: see text] is a Hom-bialgebra if and only if [Formula: see text] is a Hom-bialgebra in the category of [Formula: see text]-Yetter–Drinfeld modules [Formula: see text], generalizing the well-known Majid’s conclusion.

scholarly journals INVOLUTORY HOPF ALGEBRAS AND 3-MANIFOLD INVARIANTS

1991 ◽  
Vol 02 (01) ◽  
pp. 41-66 ◽  
Author(s):  
GREG KUPERBERG
Keyword(s):  
Hopf Algebra ◽  
Fundamental Group ◽  
Group Algebra ◽  
Hopf Algebras ◽  
Tensor Products ◽  
State Model ◽  
Formal Expression ◽  
Finite Dimensional ◽  
Heegaard Diagram ◽  
Structure Tensors

We establish a 3-manifold invariant for each finite-dimensional, involutory Hopf algebra. If the Hopf algebra is a group algebra G, the invariant counts homomorphisms from the fundamental group of the manifold to G. The invariant can be viewed as a state model on a Heegaard diagram or a triangulation of the manifold. The computation of the invariant involves tensor products and contractions of the structure tensors of the algebra. We show that every formal expression involving these tensors corresponds to a unique 3-manifold modulo a well-understood equivalence. This raises the possibility of an algorithm which can determine whether two given 3-manifolds are homeomorphic.

Hopf-galois theory and tensor products of hopf algebras

1995 ◽  
Vol 23 (11) ◽  
pp. 4009-4030 ◽  
Author(s):  
H.F. Kreimer
Keyword(s):  
Hopf Algebras ◽  
Galois Theory ◽  
Tensor Products

Tensor products of witt hopf algebras

1976 ◽  
Vol 4 (8) ◽  
pp. 761-773 ◽  
Author(s):  
Kenneth Newman
Keyword(s):  
Hopf Algebras ◽  
Tensor Products

scholarly journals Tensor products of ideal codes over Hopf algebras

2013 ◽  
Vol 56 (4) ◽  
pp. 737-744
Author(s):  
J. M. García-Rubira ◽  
J. A. López-Ramos
Keyword(s):  
Hopf Algebras ◽  
Tensor Products

HOPF ALGEBRAS OF SYMMETRIC FUNCTIONS AND TENSOR PRODUCTS OF SYMMETRIC GROUP REPRESENTATIONS

1991 ◽  
Vol 01 (02) ◽  
pp. 207-221 ◽  
Author(s):  
JEAN-YVES THIBON
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Symmetric Group ◽  
Hopf Algebras ◽  
Symmetric Functions ◽  
Tensor Products ◽  
Ring Structure ◽  
Algebra Structure ◽  
Group Representations ◽  
Symmetric Group Representations

The Hopf algebra structure of the ring of symmetric functions is used to prove a new identity for the internal product, i.e., the operation corresponding to the tensor product of symmetric group representations. From this identity, or by similar techniques which can also involve the λ-ring structure, we derive easy proofs of most known results about this operation. Some of these results are generalized.

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