Subspace Semigroups
by
Artur Bielecki
Warsaw University

Let A be an associative algebra over a field k. Let S(A) be the set of all k-subspaces of A, with multiplication:

V * W=spank{vw : v in V, w in W}.

We call S(A) the subspace semigroup of A.

Among other approaches to S(A) are the following: study the structure of S(A) and treat S(A) as an invariant of A. We present examples, problems and results that ilustrate them. In particular, we show an example of two non-isomorphic algebras such that their subspace semigroups are isomorphic, and present a theorem about the structure of S(A) for finite dimensional algebras over an algebraically closed field ([1]).

References:

1]

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. Okninski, M.S.Putcha, Subspace semigroups, preprint (to appear in J. Algebra)

Date received: August 10, 2000