A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) o...A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.展开更多
In this paper we give necessary and sufficient conditions for a comodule magma over a weak Hopf quasigroup to have a total integral,thus extending the theories developed in the Hopf algebra,weak Hopf algebra and non-a...In this paper we give necessary and sufficient conditions for a comodule magma over a weak Hopf quasigroup to have a total integral,thus extending the theories developed in the Hopf algebra,weak Hopf algebra and non-associative Hopf algebra contexts.From this result we also deduce a version of Maschke’s theorems for right(H,B)-Hopf triples associated to a weak Hopf quasigroup H and a right H-comodule magma B.展开更多
We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a,symmetric monoidal category C.li H possesses an adjoint quasiaction,we show that symmetric Yetter-Drin...We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a,symmetric monoidal category C.li H possesses an adjoint quasiaction,we show that symmetric Yetter-Drinfeld categories are trivial,and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over H and the category of four-angle Hopf modules over H under some suitable conditions.展开更多
基金Supported by NSFC grant No. 10371002 (Y. Chang) and No.19901008 (J. Lei)
文摘A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.
基金supported by Ministerio de Economía y Competi-tividad(Spain),grant MTM2016-79661-P(AEI/FEDER,UE,support included).
文摘In this paper we give necessary and sufficient conditions for a comodule magma over a weak Hopf quasigroup to have a total integral,thus extending the theories developed in the Hopf algebra,weak Hopf algebra and non-associative Hopf algebra contexts.From this result we also deduce a version of Maschke’s theorems for right(H,B)-Hopf triples associated to a weak Hopf quasigroup H and a right H-comodule magma B.
基金supported by the National Natural Science Foundation of China(Grant No.11871144)the NNSF of Jiangsu Province(No.BK20171348)the Scientific Research Foundation of Nanjing Institute of Technology(No.YKJ202040).
文摘We introduce the notions of a four-angle Hopf quasimodule and an adjoint quasiaction over a Hopf quasigroup H in a,symmetric monoidal category C.li H possesses an adjoint quasiaction,we show that symmetric Yetter-Drinfeld categories are trivial,and hence we obtain a braided monoidal category equivalence between the category of right Yetter-Drinfeld modules over H and the category of four-angle Hopf modules over H under some suitable conditions.
基金The National Natural Science Foundation of China( No. 10971188 )the Natural Science Foundation of Zhejiang Province(No.Y6110323)+2 种基金Jiangsu Planned Projects for Postdoctoral Research Funds(No. 0902081C)Zhejiang Provincial Education Department Project (No.Y200907995)Qiantang Talents Project of Science Technology Department of Zhejiang Province (No. 2011R10051)
