We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial f of degree d, there are exactly 2 distinct degree d polynomials with the same set of cyclic resultants as f . However, in the generic monic case, degree d polynomials are uniquely determined by their cyclic resultants. Moreover, two reciprocal (“palindromic”) polynomials giving rise to t...

We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial f of degree d, there are exactly 2 distinct degree d polynomials with the same set of cyclic resultants as f . However, in the generic monic case, degree d polynomials are uniquely determined by their cyclic resultants. Moreover, two reciprocal (“palindromic”) polynomials giving rise to t...

We present two noncommutative algebras over a field of characteristic zero that each possesses family actions by cyclic groups order $2n$, represented in $2 \times 2$ matrices, requiring generators degree $3n$.

We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain ⊗̂-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuou...

In this work we develop the family of Prometheus orthonormal sets (PONS) in the framework of certain abelian group algebras. Classical PONS, considered in 1991 by J. S. Byrnes, turned out to be a rediscovery of the 1960 construction by G. R. Welti [28], and of subsequent rediscoveries by other authors as well. This construction highlights the fundamental role played by group characters in the t...

The review is devoted to nonassociative algebras, rings and modules over them. main actual recent trends in this area are described. Works reviewed on radicals rings, algebras related with skew polynomials, commutative their modules, cyclic obtained as extensions, Ore extensions of hom-associative them, von Neumann finiteness for algebras. Furthermore, there outlined them harmonic analysis nonl...

A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras H(2 : n;ω2) (of dimension one less than a power of p) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of H(2 : n;ω2) with a Block algebra. W...

We prove that, for every extension of Banach algebras 0 → B → A → D → 0 such that B has a left or right bounded approximate identity, the existence of an associated long exact sequence of Banach simplicial or cyclic cohomology groups is equivalent to the existence of one for homology groups. It follows from the continuous version of a result of Wodzicki that associated long exact sequences exis...

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one be...

This is a contribution to the project of quiver approaches to quasi-quantum groups initiated in [13]. We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations. This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras, or equivalently cofree pointed coalgebras, and helps to provide a projective representation-theoretic ...