Monomial Hopf algebras over fields of positive characteristic

In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n) are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.     

Morita–Takeuchi Contexts Acting on Graded Coalgebras

In this paper, we introduce the concept of graded Morita–Takeuchi contexts and prove that every graded Morita–Takeuchi context induces a Morita–Takeuchi context between the 1-components of the corresponding coalgebras. We also establish an action of Morita–Takeuchi contexts on graded coalgebras, which is important for the development of the action of Picard groups on graded coalgebras.Partially supported by the NNSF of China and the YNSF of Shandong Province (No. Q98A05113).1991 Mathematics Subject Classification: 16W30, 16W50, 16D90     

EQUIVALENCE OF x-HOPF ALGEBRAS

Some basic properties of the antipode of an N0I-graded x-Hopf algebra are studied. Also, several equivalent conditions of an N0I-graded x-bialgebra (x-Hopf algebra) are given.     

弱模余代数的结构定理

设H为弱Hopf代数,C为弱右H-模余代数,令C=C/C·ker L.利用Smash余积来研究弱模余代数上的结构定理,并给出了C与C×H作为余代数同构的条件.     

Structures of Malcev Bialgebras on a Simple Non-Lie Malcev Algebra

In this work we consider Malcev bialgebras. We describe all structures of a Malcev bialgebra on a simple non-Lie Malcev algebra.     

Embedding of Jordan Copairs into Lie Coalgebras

Let (V, Δ) be a Jordan copair over a field Φ and let V? be its dual pair. Then there exists a Lie coalgebra (L ^c (V), Δ _L ) whose dual algebra (L ^c (V))? is the Kantor–Koecher–Tits construction for the pair V?. If Φ is a field of characteristic other than 2 or 3 then the Lie coalgebra (L ^c (J), Δ _L ) is locally finite-dimensional. As a corollary we derive that Jordan copairs over fields of characteristic other than 2 or 3 are locally finite-dimensional.     

Jordan (Super)Coalgebras and Lie (Super)Coalgebras

We discuss the question of local finite dimensionality of Jordan supercoalgebras. We establish a connection between Jordan and Lie supercoalgebras which is analogous to the Kantor–Koecher–Tits construction for ordinary Jordan superalgebras. We exhibit an example of a Jordan supercoalgebra which is not locally finite-dimensional. Show that, for a Jordan supercoalgebra (J,) with a dual algebra J ^*, there exists a Lie supercoalgebra (L ^c (J), _L ) whose dual algebra (L ^c (J))^* is the Lie KKT-superalgebra for the Jordan superalgebra J ^*. It is well known that some Jordan coalgebra J ⁰ can be constructed from an arbitrary Jordan algebra J. We find necessary and sufficient conditions for the coalgebra (L ^c (J ⁰),_L) to be isomorphic to the coalgebra (Loc(L _in (J)⁰), _L ⁰), where L _in (J) is the adjoint Lie KKT-algebra for the Jordan algebra J.     

A Degeneracy Criterion for A∞-Structures

In the paper conditions are found under which the A-structure on the homology of a differential algebra degenerates. Examples of such algebras are given. In particular, it is shown that the A-algebra structure on the Milnor coalgebra degenerates, and that if the cohomology of a topological space is a polynomial algebra, then the A-algebra structure on it degenerates.     

关于Novikov余代数

通过研究Novikov代数的对偶结构,主要讨论Novikov余代数的张量积以及Novikov代数和Novikov余代数之间的对偶关系,同时,也讨论了Novikov双代数。     

三角Hopf代数模范畴上的Lie结构间的对偶

在三角Hopf代数模范畴上研究Lie代数和Lie余代数．主要给出了Lie代数与Lie余代数间的对偶关系．