Related papers: An algebraic approach to finite projective planes
In this paper, we introduce relative Rota-Baxter systems on Leibniz algebras and give some characterizations and new constructions. Then we construct a graded Lie algebra whose Maurer-Cartan elements are relative Rota-Baxter systems. This…
To each discrete product system E of finite-dimensional Hilbert spaces we associate a C*-algebra O_E. When E is the n-dimensional product system over N, O_E is the Cuntz algebra O_n, and the irrational rotation algebras appear as O_E for…
We provide an overview of recent progress in statistical inverse problems with random experimental design, covering both linear and nonlinear inverse problems. Different regularization schemes have been studied to produce robust and stable…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…
Let A=k+A_1+A_2.... be a connected graded, noetherian k-algebra that is generated in degree one over an algebraically closed field k. Suppose that the graded quotient ring Q(A) has the form Q(A)=k(Y)[t,t^{-1},sigma], where sigma is an…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
A fake projective plane is a complex surface with the same Betti numbers as $\mathbb{C} P^2$ but not biholomorphic to it. We study the fake projective plane $\mathbb{P}_{\operatorname{fake}}^2 = (a = 7, p = 2, \emptyset, D_3 2_7)$ in the…
First we present a short overview of the long history of projectively flat Finsler spaces. We give a simple and quite elementary proof of the already known condition for the projective flatness, and we give a criterion for the projective…
In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real…
There are two seemingly unrelated ideals associated with a simplicial complex \Delta. One is the Stanley-Reisner ideal I_\Delta, the monomial ideal generated by minimal non-faces of \Delta, well-known in combinatorial commutative algebra.…
This paper studies bialgebraic structures associated with a Reynolds Leibniz algebra of weight $\lambda$, that is, a Leibniz algebra equipped with a Reynolds operator of weight $\lambda$. We first present equivalent characterizations of…
In this paper, the structure of the second relative homology and the relative stem cover of the direct sum of two pairs of Leibniz algebras are determined by means of the non-abelian tensor product of Leibniz algebras. We also characterize…
Consider ideals $I$ of the form \[ I=(x_1^2,\dots, x_n^2)+\mathrm{RLex}(x_ix_j) \] where $\mathrm{RLex}(x_ix_j)$ is the ideal generated by all the square-free monomials which are greater than or equal to $x_ix_j$ in the reverse…
This thesis concerns the algebraic consequences of Freyd's Generating Hypothesis, and explores the question of whether there exists a self-injective ring R that can be constructed purely algebraically that exhibits some of the known…
Weighted projective spaces are natural generalizations of projective spaces with a rich structure. Projective Reed-Muller codes are error-correcting codes that played an important role in reliably transmitting information on digital…
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…
In this paper, we prove the degree upper bound of projective subschemes in terms of the reduction number and show that the maximal cases are only arithmetically Cohen-Macaulay subschemes with linear resolution. Furthermore, it can be shown…
The noncommutative analog of an approximative absolute retract (AAR) is introduced, a weakly projective C*-algebra. This property sits between being residually finite dimensional and projectivity. Examples and closure properties are…
Classical Ramsey theory has successfully extended to relational structures, yielding a wealth of results that have profoundly influenced other areas of mathematics. Interestingly, the same development has not occurred in the case of dual…
The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…