Related papers: Bost-Connes systems and periodic Witt vectors
Rota-Baxter systems of T. Brzezi\'{n}ski are a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we consider Rota-Baxter systems in the…
We construct bases of the simple modules for partition algebras which are indexed by paths in an alcove geometry. This allows us to give a concrete interpretation (and new proof) of the monotone convergence property for Kronecker…
The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems ${\cal A}_n(m)$ and ${\cal C}_n(m,l)$ with integer multiplicities and corresponding algebras of quasi-invariants are investigated.…
Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our…
We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and…
Lie algebras formed via semi-direct sums of the Witt algebra $\text{Der}(\mathbb{C}[t,t^{-1}])$ and its modules have become increasingly prominent in both physics and mathematics in recent years. In this paper, we complete the study of…
In this paper, we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Groebner system in theory of Groebner…
The algebras of stable operations and cooperations in derived Witt theory with rational coefficients are computed and an additive description of cooperations in derived Witt theory is given. The answer is parallel to the well-known case of…
The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural…
It is shown that generalized Rota-Baxter operators introduced in [W.A. Martinez, E.G. Reyes & M. Ronco, Int. J. Geom. Meth. Mod. Phys. 18 (2021) 2150176] are a special case of Rota-Baxter systems [T. Brzezi\'nski, J. Algebra 460 (2016),…
The ring of Witt vectors $\mathbb{W} R$ over a base ring $R$ is an important tool in algebraic number theory and lies at the foundations of modern $p$-adic Hodge theory. $\mathbb{W} R$ has the interesting property that it constructs a ring…
The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…
Wawamoto generalized the Witt algebra using Laurent extension of polynomial ring. We construct the generalized Witt algebra $W(g_p,n)$ by using an additive map $g_p$ from a set of integers into a field of characteristic zero where $1\leq p…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
Boij-S\"oderberg theory describes the Betti diagrams of graded modules over the polynomial ring up to multiplication by a rational number. Analog Eisenbud-Schreyer theory also describes the cohomology tables of vector bundles on projective…
In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric…
We study generalized regular bent functions using a representation by bent rectangles, that is, special matrices with restrictions on rows and columns. We describe affine transformations of bent rectangles, propose new biaffine and bilinear…
We provide a variant of Baer's theorem about isomorphism of endomorphism rings of vector spaces over division rings, where the full endomorphism rings are replaced by some subrings of finitary maps.