Related papers: Automorphisms and dilation theory of triangular UH…
If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\prod A_n / \bigoplus A_n$ is called a reduced product. We prove, assuming Todorcevic's Axiom and Martin's Axiom, that every isomorphism between two reduced products of separable,…
For a perfect Lie algebra $\mathfrak{h}$ we classify all Lie algebras containing $\mathfrak{h}$ as a subalgebra of codimension $1$. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product…
We study the Hopf structure of a class of dual operator algebras corresponding to certain semigroups. This class of algebras arises in dilation theory, and includes the noncommutative analytic Toeplitz algebra and the multiplier algebra of…
Automorphisms of the canonical core UHF-subalgebra F_n of the Cuntz algebra O_n do not necessarily extend to automorphisms of O_n. Simple examples are discussed within the family of infinite tensor products of (inner) automorphisms of the…
Trialitarian automorphisms are related to automorphisms of order 3 of the Dynkin diagram of type D4. Octic etale algebras with trivial discriminant, containing quartic subalgebras, are classified by Galois cohomology with value in the Weyl…
We analyze some relations between quasi-Hopf smash products and certain twisted tensor products of quasialgebras. Along the way we obtain also some results of independent interest, such as a duality theorem for finite dimensional quasi-Hopf…
We attach to any linear endomorphism f of any vector space V a structure of prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra, the dual Hopf algebra and the associated group of characters. For f=Id\_V, we find…
A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a…
Topological algebras have properties that extend naturally to those of topological groups [8, 9], but is it the case that semi-direct products exist as in the category of groups? Firstly, we express concepts in categorical language that…
We describe the groups of automorphisms of two generated free braided associative algebras with involutive diagonal braidings over a field of characteristic $\neq 2$. Depending on the form of the diagonal involutive braiding, five different…
A Dirichlet operator algebra is a nonself-adjoint operator algebra $\mathcal{A}$ with the property that $\mathcal{A} + \mathcal{A}^*$ is norm-dense in the C$^*$-envelope of $\mathcal{A}.$ We show that, under certain restrictions,…
The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…
The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and…
We examine a certain type of abelian C*-subalgebras that allow one to give a unified treatment of two uniqueness theorems: for graph C*-algebras and for certain reduced crossed products.
Given a quasi-special endomorphism $\rho$ of a C*-algebra A with nontrivial center, we study an extension problem for automorphisms of A to a minimal cross-product B of A by $\rho$. Exploiting some aspects of the underlying generalized…
We obtain a kind of structure theorem for the automorphism group ${\rm Aut}{\cal A}$ of a unital C$^{*}$-algebra ${\cal A}$. According to it, ${\rm Aut}{\cal A}$ can be regarded as a subgroup of the semi-direct product of direct product…
We consider the motivic Hall algebra of coherent sheaves over an irreducible reduced projective curve of arithmetic genus $1$. We introduce the composition subalgebra in the singular curve case, and show that it is isomorphic to the…
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear…
The polynomial automorphisms of the affine plane over a field K form a group which has the structure of an amalgamated free product. This well-known algebraic structure can be used to determine some key results about the symmetry and…