# Group Algebras - injectivity and its generalizations

*Algebra/Geometry/Topology Seminar*

*by S.K. Jain*

*Institution:*Ohio State University, USA

*Date: Fri 6th May 2011*

*Time: 2:15 PM*

*Location: Russell Love Theatre, The University of Melbourne*

*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.

*For More Information:* contact: Craig Westerland. email: c.westerland@ms.unimelb.edu.au