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To a regular projection of a knot we associate a finite dimensional non-commutative associative algebra which is self-injective and special biserial.
This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Gr\"unbaum colorings, their existence and usage. In particular, one of the most…
We study a noncanonical Hilbert space representation of the polymer quantum mechanics. It is shown that Heisenberg algebra get some modifications in the constructed setup from which a generalized uncertainty principle will naturally come…
We introduce and study a new class of algebras, which we name \textit{quantum generalized Heisenberg algebras} and denote by $\mathcal{H}_q (f,g)$, related to generalized Heisenberg algebras, but allowing more parameters of freedom, so as…
We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…
The arithmetic of natural numbers has a natural and simple encoding within sets, and the simplest set whose structure is not that of any natural number extends this set-theoretic representation to positive and negative integers. The…
This paper systematically studies finite rank dimension groups, as well as finite dimensional ordered real vector spaces with Riesz interpolation. We provide an explicit description and classification of finite rank dimension groups, in the…
This is the second of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank. In the present part, we compare the analytic theory with the algebraic one that was begun in a paper of the third…
We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge…
Several constructive homological methods based on noncommutative Gr\"obner bases are known to compute free resolutions of associative algebras. In particular, these methods relate the Koszul property for an associative algebra to the…
Over an arbitrary field, we conduct a comprehensive study of the polynomial identities and codimensions of two- and three-dimensional metabelian non-Lie Leibniz algebras. In addition, we compute the images of multihomogeneous polynomials on…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
We present a mathematical model for a physical theory that is compatible with Einstein's Special Relativity Theory. Our model consists of three pseudo-complex dimensions, representing three real dimensions of space, dual to what could be…
The goal of this paper is to define the Grassmann integral in terms of a limit of a sum around a well-defined contour so that Grassmann numbers gain geometric meaning rather than symbols. The unusual rescaling properties of the integration…
The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…
Furstenberg-Weiss have extended Szemer\'edi's theorem on arithmetic progressions to trees by showing that a large subset of the tree contains arbitrarily long arithmetic subtrees. We study higher dimensional versions that analogously extend…
Let C be a finite dimensional algebra of global dimension at most two. A partial relation extension is any trivial extension of C by a direct summand of its relation C-C-bimodule. When C is a tilted algebra, this construction provides an…
Given a pair of distinct unitary cuspidal automorphic representations for GL(n) over a number field, let S denote the set of finite places at which the automorphic representations are unramified and their associated Hecke eigenvalues…
Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for the sample functions of a large class of self-affine random…
This work pioneers the systematic study and classification (up to Lie algebra automorphisms) of finite-dimensional coboundary Lie bialgebras through Grassmann algebras. Several mathematical structures on Lie algebras, e.g. Killing forms or…