Group Algebras - injectivity and its generalizations
by S.K. Jain
Abstract: It is well-known that the group algebra KG is self-injective if and only if G is ï¬nite. We will discuss when a semiprime CS group algebra KG of a polycyclic-by-ï¬nite group G is a direct sum of integral domains and algebras of global dimension â‰¤ 1 and what is its structure? Is this group algebra a direct sum of matrix rings over KN , where N< D_\infty analogous to known results for prime rings ? We wil also give results on continuous semilocal group algebra KG of a nilpotent group G. Finally, we will brieï¬‚y talk of self-injective generalized group algebra L^1(G, A) of a locally compact group G over a Banach algebra A with identity.
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