c](V) from the free associative algebra
of V to the free associative coalgebra of V, such that [[OHM].
and Iruing R, Representation Theory of Finite Groups and Associative Algebra
, John Wiley and Sons (1962).
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).
The universal enveloping algebra U(ST(2)) of the Lie algebra ST(2) is the associative algebra
Consequently, Rota-Baxter systems yield pre-Lie and associative algebra
xn) be a free associative algebra
with n generators x1xn over a field K.
Hochschild, On the cohomology groups of an associative algebra
L]) with an associative algebra
u(R, L), an algebra map [[iota].
An identity of an associative algebra
is a non-commuting polynomial that vanishes identically on all substitutions in the algebra, say Kanel-Belov, Karasik, and Rowen, and an identity is a polynomial identity (PI) if at least one of its coefficients is more or less than one.
q]) on the associative algebra
of strictly upper triangular matrices.
We have a classical example of such an algebra when we consider the Hochschild cohomology of an associative algebra