Related papers: Algebra of dimension theory
By a theorem due to the first author, the bounded derived category of a finite-dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra. This embedding is an equivalence iff the algebra…
For a positively graded artin algebra $A=\oplus_{n\geq 0}A_n$ we introduce its Beilinson algebra $\mathrm{b}(A)$. We prove that if $A$ is well-graded self-injective, then the category of graded $A$-modules is equivalent to the category of…
Let $Q$ be an acyclic quiver. Associated with any element $w$ of the Coxeter group of $Q$, triangulated categories $\underline{\Sub}\Lambda_w$ were introduced in \cite{Bua2}. There are shown to be triangle equivalent to generalized cluster…
It has been proposed that cobordism and K-theory groups, which can be mathematically related in certain cases, are physically associated to generalised higher-form symmetries. As a consequence, they should be broken or gauged in any…
We define a graded multiplication on the vector space of essential paths on a graph $G$ (a tree) and show that it is associative. In most interesting applications, this tree is an ADE Dynkin diagram. The vector space of length preserving…
Given a Hopf algebra $A$ graded by a discrete group together with an action of the same group preserving the grading, we define a new Hopf algebra, which we call the graded twisting of $A$. If the action is adjoint, this new Hopf algebra is…
An enhanced Leibniz algebra is an algebraic struture that arises in the context of particular higher gauge theories describing self-interacting gerbes. It consists of a Leibniz algebra $(\mathbb{V},[ \cdot, \cdot ])$, a bilinear form on…
Let $A=kQ/I$ be a finite dimensional basic algebra over an algebraically closed field $k$ which is a gentle algebra with the marked ribbon surface $(\mathcal{S}_A,\mathcal{M}_A,\Gamma_A)$. It is known that $\mathcal{S}_A$ can be divided…
This present paper has the purpose to find certain physical appications of Lobachevsky geometry and of the algebraic geometry approach in theories with extra dimensions. It has been shown how the periodic properties of the uniformization…
We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
We consider the global aspects of the 6-dimensional $\mathcal{N}=(1, 0)$ theory arising from the coupling of the vector multiplet to the tensor multiplet. We show that the Yang-Mills field and its dual, when both are abelianized, combine to…
Let $K \langle X\rangle$ be the free associative algebra freely generated over the field $K$ by the countable set $X = \{x_1, x_2, \ldots\}$. If $A$ is an associative $K$-algebra, we say that a polynomial $f(x_1,\ldots, x_n) \in K \langle…
The representation dimension was defined by M. Auslander in 1970 and is, due to spectacular recent progress, one of the most interesting homological invariants in representation theory. The precise value is not known in general, and is very…
In this paper we investigate the class of the connected graded algebras which are finitely generated in degree 1, which are finitely presented with relations of degrees greater or equal to 2 and which are of finite global dimension D and…
The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…
We develop geometry of algebraic subvarieties of $K^{n}$ over arbitrary Henselian valued fields $K$. This is a continuation of our previous article concerned with algebraic geometry over rank one valued fields. At the center of our approach…
In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…
We study algebras k[x_1,...,x_n]/I which admit a grading by a subsemigroup of N^d such that every graded component is a one-dimensional k-vector space. V.I.~Arnold and coworkers proved that for d = 1 and n <= 3 there are only finitely many…
This paper develops a cohomology theory for Hom-Jacobi-Jordan algebras using and applies it to classify non-abelian extensions. The main result establishes that equivalence classes of split extensions of a Hom-Jacobi-Jordan algebra $J$ by…