Irreducible Lie–Yamaguti algebras

Subdirectly irreducible separable dynamic algebras

A characterization of the subdirectly irreducible separable dynamic algebras is presented. The notions developed for this study were also suitable to describe the previously found class of the simple separable dynamic algebras.

Subdirectly Irreducible Quasi-modal Algebras

In this paper we give suitable notions of congruences and subdirectly irreducible algebras for the class of quasi-modal algebras introduced in [1]. We also prove some characterizations of subdirectly irreducible algebras following the similar results given by G. Sambin [5] for modal algebras.

Irreducible Representations of Operator Algebras

Irreducible Representations of Twisted Multiloop Algebras

We describe the finite-dimensional simple modules of all the twisted multiloop algebras and classify them up to isomorphism.

Constructing Irreducible Representations of Finitely Presented Algebras

We describe an algorithmic test, using the “standard polynomial identity” (and elementary computational commutative algebra), for determining whether or not a finitely presented associative algebra has an irreducible n-dimensional representation. When ndimensional irreducible representations do exist, our proposed procedure can (in principle) produce explicit constructions.