Indecomposable Representations of the Superalgebra $B(1,2)$

M. N. Trushina


Abstract: Finite-dimensional indecomposable superbimodules over the superalgebra $B(1,2)$ are treated. We propound a method for constructing indecomposable alternative superbimodules over $B(1,2)$ containing a given socle (such can be presented by any irreducible module over $B(1,2)$). The method is based on adding on the Jordan basis. Also, for the characteristic 3 case, we give examples of Jordan indecomposable superbimodules which are not alternative.

Keywords: indecomposable superbimodule, Jordan superbimodule, alternative superbimodule.

UDC: 512.554

Received: 09.08.2001

 English version: Algebra and Logic, 2002, 41:3, 207–213

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