scholarly journals Enveloping actions and duality theorems for partial twisted smash products

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3217-3227
Author(s):  
Shuangjian Guo ◽  
Xiaohui Zhang ◽  
Yuanyuan Ke ◽  
Yizheng Li
Keyword(s):  
Smash Product ◽  
Morita Context ◽  
Duality Theorems

In this paper, we first generalize the theorem about the existence of an enveloping action to a partial twisted smash product. Then we construct a Morita context between the partial twisted smash product and the twisted smash product related to the enveloping action. Finally, we present versions of the duality theorems of Blattner-Montgomery for partial twisted smash products.

SMASH PRODUCTS, SEPARABLE EXTENSIONS AND A MORITA CONTEXT OVER HOPF ALGEBROIDS

2014 ◽  
Vol 13 (04) ◽  
pp. 1350124
Author(s):  
YONG WANG ◽  
GUANGQUAN GUO
Keyword(s):  
Type Theorem ◽  
Smash Product ◽  
Module Algebra ◽  
Morita Context ◽  
Hopf Algebroid ◽  
Hopf Algebroids ◽  
Maschke Type Theorem ◽  
Module Algebras ◽  
Product Algebra ◽  
Separable Extensions

Let [Formula: see text] be a Hopf algebroid, and A a left [Formula: see text]-module algebra. This paper is concerned with the smash product algebra A#H over Hopf algebroids. In this paper, we investigate separable extensions for module algebras over Hopf algebroids. As an application, we obtain a Maschke-type theorem for A#H-modules over Hopf algebroids, which generalizes the corresponding result given by Cohen and Fischman in [Hopf algebra actions, J. Algebra100 (1986) 363–379]. Furthermore, based on the work of Kadison and Szlachányi in [Bialgebroid actions on depth two extensions and duality, Adv. Math.179 (2003) 75–121], we construct a Morita context connecting A#H and [Formula: see text] the invariant subalgebra of [Formula: see text] on A.

scholarly journals The Maschke-Type Theorem and Morita Context for BiHom-Smash Products

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Bingliang Shen ◽  
Ling Liu
Keyword(s):  
Hopf Algebra ◽  
Type Theorem ◽  
Smash Product ◽  
Morita Context ◽  
Maschke Type Theorem

Let H , α H , β H , ω H , ψ H , S H be a BiHom-Hopf algebra and A , α A , β A be an H , α H , β H -module BiHom-algebra. Then, in this paper, we study some properties on the BiHom-smash product A # H . We construct the Maschke-type theorem for the BiHom-smash product A # H and form an associated Morita context A H , A H A A # H , A # H A A H , A # H .

scholarly journals Partial (Co)actions of multiplier Hopf algebras: Morita and Galois theories

2020 ◽  
pp. 2150142
Author(s):  
Danielle Azevedo ◽  
Eliezer Batista ◽  
Graziela Fonseca ◽  
Eneilson Fontes ◽  
Grasiela Martini
Keyword(s):  
Hopf Algebras ◽  
Product Formula ◽  
Smash Product ◽  
Morita Context ◽  
Multiplier Hopf Algebras ◽  
Coinvariant Algebra

In this work, we deal with partial (co)actions of multiplier Hopf algebras on not necessarily unital algebras. Our main goal is to construct a Morita context relating the coinvariant algebra [Formula: see text] with a certain subalgebra of the smash product [Formula: see text]. Besides that, we present the notion of partial Galois coaction, which is closely related to this Morita context.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals Localization in a Morita context with applications to fixed rings

1991 ◽  
Vol 143 (2) ◽  
pp. 373-387 ◽  
Author(s):  
P Loustaunau ◽  
J Shapiro
Keyword(s):  
Morita Context

Lie ideals, Morita context and Generalized (α, β)-Derivations

2013 ◽  
Vol 33 (4) ◽  
pp. 1059-1070 ◽  
Author(s):  
S. Khalid NAUMAN ◽  
Nadeem ur REHMAN ◽  
R.M. AL-OMARY
Keyword(s):  
Morita Context

scholarly journals Symmetric dual multiobjective fractional programming

1991 ◽  
Vol 50 (1) ◽  
pp. 67-74 ◽  
Author(s):  
T. Weir
Keyword(s):  
Fractional Programming ◽  
Multiobjective Fractional Programming ◽  
Duality Theorems

AbstractA pair of symmetric dual multiobjective fractional programming problems is formulated and appropriate duality theorems are established.

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