相关论文: Adapted algebras and standard monomials

In this paper we study standard bases for submodules of a mixed power series and polynomial ring $R[[t_1,\ldots,t_m]][x_1,\ldots,x_n]^s$ respectively of their localization with respect to a $t$-local monomial ordering for a certain class of…

We classify group gradings on the simple Lie algebra $L$ of type $D_4$ over an algebraically closed field of characteristic different from 2: fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism. For…

We introduce and study the notion of the $G$-Tutte polynomial for a list $\mathcal{A}$ of elements in a finitely generated abelian group $\Gamma$ and an abelian group $G$, which is defined by counting the number of homomorphisms from…

Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate…

Let $G$ be the group scheme $\operatorname{SL}_{d+1}$ over $\mathbb{Z}$ and let $Q$ be the parabolic subgroup scheme corresponding to the simple roots $\alpha_{2},\cdots,\alpha_{d-1}$. Then $G/Q$ is the $\mathbb{Z} $-scheme of partial flags…

Let $p$ be an odd prime and let $G$ be a non-abelian finite $p$-group of exponent $p^2$ with three distinct characteristic subgroups, namely $1$, $G^p$, and $G$. The quotient group $G/G^p$ gives rise to an anti-commutative ${\mathbb…

A Lie group G has many left invariant metrics having drastically different curvature properties. If we regard G as a flat and globalizable absolute parallelism as in [O1], then G has a canonical metric. We study some surprising consequences…

We introduce the notion of a regular action in the category of conformal modules over Lie conformal algebras with Virasoro elements. We show that a finite conformal module over the general conformal algebra $\mathfrak{gc}_1$ (resp.,…

Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of…

In this paper, we introduce the notion of modular class of a Lie algebroid $A$ equipped with a Nambu structure satisfying some suitable hypothesis. We also introduce cohomology and homology theories for such Lie algebroids and prove that…

The purpose of this paper is to study $W(2,2)$ Lie conformal algebra, which has a free $\mathbb{C}[\partial]$-basis $\{L, M\}$ such that $[L_\lambda L]=(\partial+2\lambda)L$, $[L_\lambda M]=(\partial+2\lambda)M$, $[M_\lambda M]=0$. In this…

Given an algebraic Lie algebra $\mathfrak{g}$ over $\mathbb{C}$, we canonically associate to it a Lie algebra $\mathfrak{g}_{\infty}$ defined over $\mathbb{C}_{\infty}$-the reduction of $\mathbb{C}$ mod infinitely large prime, and show that…

For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple Lie algebras of types A_n (n >= 1), B_n (n >= 2), C_n (n >= 3) and D_n (n > 4), in terms of numerical and group-theoretical invariants. The ground…

We construct a canonical frame for an arbitrary Gl(2)-structure thus solving the equivalence problem for Gl(2)-structures. Our treatment includes also a problem of contact equivalence of ordinary differential equations and applies to…

We consider the standard modules of rectangular highest weights of affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. By using vertex algebraic techniques we construct the combinatorial bases for standard modules and their…

We classify gradings by arbitrary abelian groups on the classical simple Lie and Jordan superalgebras $Q(n)$, $n \geq 2$, over an algebraically closed field of characteristic different from $2$ (and not dividing $n+1$ in the Lie case): fine…

For any abelian group $G$, we classify up to isomorphism all $G$-gradings on the classical central simple Lie algebras, except those of type $D_4$, over the field of real numbers (or any real closed field).

We show how the relation between $Q$-manifolds and Lie algebroids extends to ``higher'' or ``non-linear'' analogs of Lie algebroids. We study the identities satisfied by a new algebraic structure that arises as a replacement of operations…

For a type I basic classical Lie superalgebra $\mathfrak{g}=\mathfrak{g}_{\bar{0}} \oplus \mathfrak{g}_{\bar{1}}$, we establish an equivalence between typical blocks of categories of $U_{\chi}(\mathfrak{g})$-modules and…

For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…