Related papers: Non-associative versions of Hilbert's basis theore…

Given a pair of nilpotent Lie algebras $A$ and $B$, an extension $0\xrightarrow{} A\xrightarrow{} L\xrightarrow{} B\xrightarrow{} 0$ is not necessarily nilpotent. However, if $L_1$ and $L_2$ are extensions which correspond to lifts of a map…

We introduce some modified forms for the degenerate and non-degenerate affine Hecke algebras of type $A$. These are certain subalgebras living inside the inverse limit of cyclotomic Hecke algebras. We construct faithful representations and…

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of…

In the theory of combinatorial algebras, there is a sequence of embeddings between Kleene's second model, van Oosten's model, and Scott's graph model. We prove that none of these embeddings can be reversed. We also prove nonembedding…

Relationship is clarified between the notions of linear extension of algebraic theories, and central extension, in the sense of commutator calculus, of their models. Varieties of algebras turn out to be nilpotent Maltsev precisely when…

In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Groebner-Shirshov bases of free Rota-Baxter algebra, $\lambda$-differential algebra and…

This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in the relative situation over a noncentral, noncommutative, nonsemisimple base ring, as announced in Section 0.4 of arXiv:0708.3398. We prove the…

In this paper, using the general Mal'cev-Neumann construction of Laurent series rings, we construct a Laurent series ring with a base ring which is an extension of the field $\mathbb{Q}$ of rational numbers. Further, we establish some…

Symmetric rings were introduced by Lambek to extend usual commutative ideal theory in noncommutative rings. In this paper, we study symmetric rings over which Ore extensions are symmetric. A ring R is called strongly \sigma-symmetric if the…

In this paper we present a right version of the algorithms developed for to compute Gr\"obner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right…

We prove a non-commutative version of the Hilbert's 17th problem, giving a characterization of the class of non-commutative polynomials in n-undeterminates that have positive trace when evaluated in n-selfadjoint elements in arbitrary II1…

Let $q$ be any prime $\equiv 7 \mod 16$, $K = \mathbb{Q}(\sqrt{-q})$, and let $H$ be the Hilbert class field of $K$. Let $A/H$ be the Gross elliptic curve defined over $H$ with complex multiplication by the ring of integers of $K$. We prove…

A basis of Lorentz and gauge-invariant monomials in non--Abelian gauge theories with matter is described, applicable for the inverse mass expansion of effective actions. An algorithm to convert an arbitrarily given invariant expression into…

We prove a number field analogue of the Green--Tao--Ziegler theorem on simultaneous prime values of degree 1 polynomials whose linear parts are pairwise linearly independent. Applications of our results include a Hasse principle of rational…

We set up an algebraic framework for the study of pseudoholomorphic discs bounding nonorientable Lagrangians, as well as equivariant extensions of such structures arising from a torus action. First, we define unital cyclic twisted…

We present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of non-attacking rooks that can be placed on the polyomino. By using a computational approach, we…

We address the problem of constructing the non-associative version of the Dynkin form of the Baker-Campbell-Hausdorff formula; that is, expressing $\log (\exp (x)\exp(y))$, where $x$ and $y$ are non-associative variables, in terms of the…

It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the…

Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations…

Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known…