Related papers: Large annihilators in Cayley-Dickson algebras II
We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective…
We believe we have made progress in the age-old problem of divisibility rules for integers. Universal divisibility rule is introduced for any divisor in any base number system. The divisibility criterion is written down explicitly as a…
From the viewpoints of the division by zero $1/0=0/0=z/0=0$ and the division by zero calculus, we will examine the mysterious properties of the point at infinity in the sense of the Alexandroff one compactification of the complex plane…
In our previous publications we have introduced analogs of partial derivatives on the algebras U(gl(N)). In the present paper we compare two methods of introducing these analogs: via the so-called quantum doubles and by means of a…
We give a counterexample and some conclusions for effective non-vanishing of Weil divisors on algebraic surfaces.
We introduce what we call "alternative twisted tensor products" for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-Dickson process, the Clifford process and the twisted tensor…
In this paper, we continue our study of the zero-divisor graphs of lower dismantlable lattices that was started in [20]. The present paper mainly deals with an Isomorphism Problem for the zero-divisor graphs of lattices. In fact, we prove…
It is well known that central simple algebras are split by suitable finite Galois extensions of their centers. A counterpart of this result was studied by Juan and Magid in the set up of differential matrix algebras, wherein Picard-Vessiot…
A generalized inverse problem for a two-dimensional difference operator is introduced. A new construction of the algebro-geometric difference operators of two types first considered by I.M.Krichever and S.P.Novikov is proposed
The Cayley-Dickson loop Q_n is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley-Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers,…
In this paper, we give an efficient algorithm to compute the Gelfand-Kirillov dimensions of simple highest weight modules of exceptional Lie algebras. By using the Sommers-Achar duality, we also determine the annihilator varieties of these…
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
A method of determining two factors of an odd integer without need of multiplication or division operation in iterative portion of computation is presented. It is feasible for an implementing algorithm to use only integer addition and…
We use Galois descent to construct central extensions of twisted forms of split simple Lie algebras over rings. These types of algebras arise naturally in the construction of Extended Affine Lie Algebras. The construction also gives…
The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and…
In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…
Algebras of derived dimension zero are known.
We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti--self--dual Yang--Mills equations with a gauge group Diff$(S^1)$.
In this paper will be proved an inequality regarding $v_2(a^{b}-c^{d})$. Using this formula it will be possible to have informations about the divisibility of 2 of this function without computing it. Then, will be studied the behavior of…
Let $C \geq 1$. Inspired by the LLL-algorithm, we define strongly $C$-reduced divisors of a number field $F$ which are generalized from the concept of reduced Arakelov divisors. Moreover, we prove that strongly $C$-reduced Arakelov divisors…