by Caenepeel, S.; Van Oystaeyen, F.; Zhou, Borong

We investigate how the category of Doi-Hopf modules can be made into a monoidal category. It suffices that the algebra and coalgebra in question are both bialgebras with some extra compatibility relation. We study tensor identies for monoidal categories of Doi-Hopf modules. Finally, we construct braidings on a monoidal category of Doi-Hopf modules. Our construction unifies quasitriangular and coquasitriangular Hopf algebras, and Yetter-Drinfel’d modules.

DOI: 10.1023/A:1009916416083
Print publication date: 3/1/1998
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by Fan, Yun; Puig, Lluis

For modular group algebras over an arbitrary field we define new type of blocks: blocks with nilpotent extensions, and describe their source algebras. To do it, a general pattern is proposed for relations between the source algebra of a block and the source algebra of a block appearing in its decomposition in a suitable extension of the field of coefficients.

DOI: 10.1023/A:1009964332013
Print publication date: 3/1/1998
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by Mazorchuk, V. S.; Ovsienko, S. A.

For complex Lie algebra sl(n, C) we study the submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules over some subalgebra of type sl(k, C). We obtain necessary and sufficient conditions for the existence of a submodule generalizing the Bernstein-Gelfand-Gelfand theorem for Verma modules.

DOI: 10.1023/A:1009929615175
Print publication date: 3/1/1998
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by

DOI: 10.1023/A:1017108231104
Print publication date: 3/1/1998
View article on SpringerLink