A b s t r a c t. We investigate some properties of two varieties of algebras arising from quantum computation quasi-MV algebras and √ ′ quasi-MV algebras first introduced in [13], [12] and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of √ ′ quasiMV algebras...

We announce recent progress on the question about the semisolvability of semisimple Hopf algebras of dimension < 60. 2000 AMS Subject Classification: 16W30

both greatly acknowledge the hospitality of the RSISE.

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside categories are also modular. As consequence, we obtain conditions under which relative monoidal centers give (non-semisimple) categories, and show that examples include representation small quantum groups. further derive representations more general groups, braide...

Commutative Hilbertian Frobenius algebras are those commutative semigroup objects in the monoidal category of Hilbert spaces, for which adjoint multiplication satisfies compatibility relation, that is, this “comultiplication” is a bimodule map. In note we show relation forces operators to be normal. We then prove these have strong Wedderburn decomposition where (ortho)complement Jacobson radica...

We show that finite-dimensional Lie algebras over a field of characteristic zero such that the second cohomology group in every finite-dimensional module vanishes, are, essentially, semisimple.

We describe all locally semisimple subalgebras and all maximal subalgebras of the finitary Lie algebras gl(∞), sl(∞), so(∞), and sp(∞). For simple finite–dimensional Lie algebras these classes of subalgebras have been described in the classical works of A. Malcev and E. Dynkin.

In this paper we study the partial Brauer C-algebras Rn(δ, δ ), where n ∈ N and δ, δ ∈ C. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction Rn−1 →֒ Rn. We also determine the corresponding decomposition matrix, and the Cartan decomposition matrix.

We extend Guillemin and Sternberg’s Realization Theorem for transitive Lie algebras of formal vector fields to certain Lie algebras of formal first order differential operators, and show that Blattner’s proof of the Realization Theorem allows for a computer implementation that automatically reproduces many realizations derived in the existing literature, and that can also be used to compute new...

A famous lower bound for the bilinear complexity of the multiplication in associative algebras is the Alder–Strassen bound. Algebras for which this bound is tight are called algebras of minimal rank. After 25 years of research, these algebras are now well understood. We here start the investigation of the algebras for which the Alder–Strassen bound is off by one. As a first result, we completel...