Hom-associative algebras generalize the concept of associative algebras
. They were introduced by Makhlouf and Silvestrov in .
It is well-known that Lie algebras are related to associative algebras
via the commutator bracket construction.
Skowronski and Yamagata examine representation theory of finite dimensional associative algebras
with an identity over a field, which currently can be regarded as the study of the categories of their finite dimensional modules and the associated combinatorial and homological invariants.
Now, it is interesting to note that there is a class of algebras which is nonassociative and noncommutative but possesses many characteristics similar to commutative and associative algebras
and has close relations with commutative algebras.
2 Curved Rota-Baxter systems and associative algebras
Skowronski, Elements of the representation theory of associative algebras
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.
Comparison of deformations and geometric study of associative algebras
Molev (University of Sydney) describes the structure and properties of Yangian and twisted Yangian associative algebras
. The monograph proves classification theorems for the irreducible finite-dimensional representations of both algebras, develops explicit constructions of finite-dimensional irreducible representations of the Yangian, and applies Yangian theory to classical Lie algebras.
Pierce, Associative Algebras
, Springer-Verlag, New York, 1982.
Rota-Baxter operators (on associative algebras
) were introduced by Baxter to solve an analytic formula in probability [1-4].
Bremner and Dotsenko introduce concrete methods for working with associative structures of all sorts, most notably commutative associative algebras
, noncommutative associative algebras
, and operads.