One checks that M(A) is itself an

associative algebra with unit element under the following operations:

By a topological algebra we mean a topological vector space A over K, which is also an

associative algebra over K such that the multiplication in A is separately continuous (1).

Note that u is not an

associative algebra, although it is closed under the Lie bracket.

We have a classical example of such an algebra when we consider the Hochschild cohomology of an

associative algebra [1].

It is an

associative algebra with identity given by the diagram corresponding to {{1, 1'}, .

Their main examples of these Hopf-power chains were inverse shuffling (from the free

associative algebra, with states indexed by its usual word basis) and rock-breaking (from the algebra of symmetric functions, with states indexed by the elementary symmetric functions {[e.

k] be the linear operator on the free

associative algebra K<A> (over some field K) defined by

How to compute the wedderburn decomposition of a finite-dimensional

associative algebra.

That is, MR is the free

associative algebra on two sequences ([S.

xn) be a free

associative algebra with n generators x1xn over a field K.

Skowronski, Elements of the representation theory of

associative algebras, vol.

They cover gradings on algebras,

associative algebras, classical Lie algebras, composition algebras and type G2, Jordan algebras with type F4, other simple Lie algebras in characteristic zero, and Lie algebras of Caran type in prime characteristic.