Related papers: On conjugate systems with respect to completely po…
Multiple polylogarithms are equipped with rich algebraic structures including the motivic coaction and the single-valued map which both found fruitful applications in high-energy physics. In recent work arXiv:2312.00697, the current authors…
We present geometric characterizations of the partial isometries, unitaries, and invertible operators in C*-algebras and von Neumann algebras.
Partial dynamical systems (X,alpha) arise naturally when dealing with commutative C*-dynamical system (A,delta). We associate with every pair (X,alpha), or (A,delta), a covariance C*-algebra C*(X,alpha)=C*(A,delta) which agrees with a…
Jurij Vol\v{c}i\v{c} conjectured that a noncommutative polynomial $g$ belongs to the unital $\mathbb{K}$-algebra generated by finitely many noncommutative polynomials if and only if, for matrices of every size, every joint invariant…
We study covariance matrix estimation for the case of partially observed random vectors, where different samples contain different subsets of vector coordinates. Each observation is the product of the variable of interest with a $0-1$…
A fresh approach to the long debated question is proposed, starting from the GRAM-BACKLUND analytical continuation of the Zeta function (G-B Zeta expression). Consideration is given to the symmetric (even-exponent) and anti-symmetric (odd…
Several techniques together with some partial answers are given to the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras.
We apply Hilbert module methods to show that normal completely positive maps admit weak tensor dilations. Appealing to a duality between weak tensor dilations and extensions of CP-maps, we get an existence proof for certain extensions. We…
We prove that for any fixed unitary matrix $U$, any abelian self-adjoint algebra of matrices that is invariant under conjugation by $U$ can be embedded into a maximal abelian self-adjoint algebra that is still invariant under conjugation by…
We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states and also intertwine their automorphism…
A gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A is an N-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential)…
We show that any two Hadamard subfactors arising from a pair of distinct complex Hadamard matrices of order 3 are either equal or conjugate by a unitary in the relative commutant of their intersection. Moreover, when the Hadamard subfactors…
This paper is concerned with derivations in algebras of (unbounded) operators affiliated with a von Neumann algebra $\mathcal{M}$. Let $\mathcal{% A}$ be one of the algebras of measurable operators, locally measurable operators or, $\tau…
We analize the algebraic structure of consistent and covariant anomalies in gauge and gravitational theories: using a complex extension of the Lie algebra it is possible to describe them in a unified way. Then we study their representations…
We consider various lifting problems for C*-algebras. As an application of our results we show that any commuting family of order zero maps from matrices to a von Neumann central sequence algebra can be lifted to a commuting family of order…
In this paper motivated by the celebrated fundamental theorem of algebra and its standard proof utilizing Liouville's Theorem, we prove the fundamental theorem of algebra type results for both commutative and noncommutative polynomials in…
Recently, Hartz proved that every commuting contractive classical multishift with non-zero weights satisfies the matrix-version of von Neumann's inequality. We show that this result does not extend to the class of commuting operator-valued…
We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…
We derive formulae for Gram matrices arising in the Nyman--Beurling reformulation of the Riemann hypothesis. The development naturally leads upon series of the form $S(x) = \sum_{n\ge 1} R(nx)$ and their reciprocity relations. We give…
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is…