Talk:Brauer algebra

Is this a monoid?
Something that's unclear to me from the description in this article, and probably should be made more clear: is the Brauer algebra just a monoid (the monoid of pairings with the given associative binary operation, and with the identity element being the pairing that matches X_i to Y_i) or is it the associated monoid ring? For instance, if it's the monoid rather than the monoid algebra, it would be fair to say that it contains the symmetric group as a submonoid, right? Is it the same as the Brauer monoid described in e.g. 10.1007/BF02304173? —David Eppstein (talk) 03:11, 29 March 2009 (UTC)