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We prove that the number of geometrically indecomposable representations of fixed dimension vector d of a canonical algebra C defined over a finite field Fq is given by a polynomial in q (depending on C and d). We prove a similar result for…
Contrary to the finite-dimensional case, the Moebius group admits interesting self-representations when infinite-dimensional. We construct and classify all these self-representations. The proofs are obtained in the equivalent setting of…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
We introduce quantum Borcherds-Bozec superalgebras. We present and prove various results of the quantum superalgebras including a bilinear form, higher Serre relation, quasi-R-matrix, character formula for the irreducible highest weight…
We show that for acylindrically hyperbolic groups $\Gamma$ (with no nontrivial finite normal subgroups) and arbitrary unitary representation $\rho$ of $\Gamma$ in a (nonzero) uniformly convex Banach space the vector space…
We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.
We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to 2.
Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
In this paper we prove that there exist infinitely many integers which can be expressed as a sum of four cubes of polynomials with integer coefficients. We give several identities that express the integers 1 and 2 as a sum of four cubes of…
We show that cylindric polyadic algebras introduced by Ferenczi has the superamalgmation property. We give two proofs. One is a Henkin construction, and the other is inspired by duality theory in modal logic between finite zig zag products…
We study the representability of sets that admit extended formulations using mixed-integer bilevel programs. We show that feasible regions modeled by continuous bilevel constraints (with no integer variables), complementarity constraints,…
We introduce a class of monotone $\sigma$-complete effect algebras, called representable, which are $\sigma$-homomorphic images of a class of monotone $\sigma$-complete effect algebras of functions taking values in the interval $[0,1]$ and…
We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these…
In the variety of all linear algebras over the infinite field the difference between geometric and automorphic equivalence of algebras can be big.
A classification of all four-dimensional power-commutative real division algebras is given. It is shown that every four-dimensional power-commutative real division algebra is an isotope of a particular kind of a quadratic division algebra.…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…
We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…
We prove that entire bounded monotone solutions to a certain class of fully nonlinear equations in 2D are one-dimensional. Our result also gives a new (non-variational) proof of the well known De Giorgi's conjecture.