Related papers: The integral polytope group

The reduced norm-one group G of a central simple algebra is an inner form of the special linear group, and an involution on the algebra induces an automorphism of G. We study the action of such automorphisms in the cohomology of arithmetic…

ABSTRACT. Let $\Phi$ be a finite dimensional $K$-algebra and let $\mathscr{C} = \textrm{mod}\: \Phi$ be the abelian category of finitely generated right $\Phi$-modules. In their 1985 paper ``Modules determined by their composition…

We consider nilpotent Lie groups for which the derived subgroup is abelian. We equip them with subRiemannian metrics and we study the normal Hamiltonian flow on the cotangent bundle. We show a correspondence between normal trajectories and…

We let S denote the ring of polynomial functions on the space of m x n matrices, and consider the action of the group GL = GL_m x GL_n via row and column operations on the matrix entries. For a GL-invariant ideal I in S we show that the…

In this paper, we study the connected blocks polytope, which, apart from its own merits, can be seen as the generalization of certain connectivity based or Eulerian subgraph polytopes. We provide a complete facet description of this…

The classical theorem of Weitzenboeck states that the algebra of invariants of a single unipotent transformation $g$ in $GL_m(K)$ acting on the polynomial algebra $K[x_1,...,x_m]$ over a field $K$ of characteristic 0 is finitely generated.…

We determine Grothendieck groups of periodic derived categories. In particular, we prove that the Grothendieck group of the $m$-periodic derived category of finitely generated modules over an Artin algebra is a free $\mathbb{Z}$-module if…

In this paper we develop a Grobner bases theory for ideals of partial difference polynomials with constant or non-constant coefficients. In particular, we introduce a criterion providing the finiteness of such bases when a difference ideal…

Consider the Grothendieck group of finite type projective modular representations of the symmetric groups on n letters, or more generally, of its wreath product with a finite group. They form a graded group, with a product defined using…

Let p be a prime and q=p^g. We show that the Grothendieck ring of finitely generated F_{q}[SL(2,F_{q})]-modules is naturally isomorphic to the quotient of the polynomial algebra Z[x] by the ideal generated by f^[g](x)-x, where…

We construct the quantized enveloping algebra of any simple Lie algebra of type ADE as the quotient of a Grothendieck ring arising from certain cyclic quiver varieties. In particular, the dual canonical basis of a one-half quantum group…

We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection…

We introduce a general constructive method to find a p-basis (and the Ulm invariants) of a finite Abelian p-group M. This algorithm is based on Groebner bases theory. We apply this method to determine the additive structure of…

Let $G$ be the mapping torus of a polynomially growing automorphism of a finitely generated free group. We determine which epimorphisms from $G$ to $\mathbb{Z}$ have finitely generated kernel, and we compute the rank of the kernel. We thus…

The abelianization is a functor from groups to abelian groups, which is left adjoint to the inclusion functor. Being a left adjoint, the abelianization functor commutes with all small colimits. In this paper we investigate the relation…

The automorphism group of a particular free spectrahedron is determined via a novel argument involving algebraic methods.

We investigate a geometric approach to determining the complete set of numerators giving rise to finite Feynman integrals. Our approach proceeds graph by graph, and makes use of the Newton polytope associated to the integral's Symanzik…

We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the "Euler characteristic integral" of a certain cohomotopy class over its scheme of…

We extend the theory of bilinear forms on the Green ring of a finite group developed by Benson and Parker to the context of the Grothendieck group of a triangulated category with Auslander-Reiten triangles, taking only relations given by…

Let F be a non-Archimedean locally compact field with residual characteristic p, let G be an inner form of GL(n,F) for a positive integer n and let R be an algebraically closed field of characteristic different from p. When R has…