Related papers: Mackey algebras which are Gorenstein

Let $R={\sf k}[x,y,z]$, the polynomial ring over a field $\sf k$. Several of the authors previously classified nets of ternary conics and their specializations over an algebraically closed field. We here show that when $\sf k$ is…

Let $H$ be a separable real Hilbert space. Denote by ${\mathcal G}_{\infty}(H)$ the Grassmannian consisting of closed subspaces with infinite dimension and codimension. This Grassmannian is partially ordered by the inclusion relation. We…

Let $K\langle X_d\rangle$ be the free associative algebra of rank $d \geq 2$ over a field $K$. Lane in 1976 and Kharchenko in 1978 proved that the algebra of invariants $K\langle X_d\rangle^G$ is free for any subgroup $G \leq…

A finite group is said to have "perfect order classes" if the number of elements of any given order is either zero or a divisor of the order of the group. The purpose of this note is to describe explicitly the finite Hamiltonian groups with…

For the Klein-Four Group $G$ and a perfect field $k$ of characteristic two we determine all indecomposable symplectic $kG$-modules, that is, $kG$-modules with a symplectic, $G$-invariant form which do not decompose into smaller such…

We consider Borcherds algebras with no real roots and the property that all zeroes in the Borcherds Cartan matrix occur in a single diagonal zero block. It follows that all other entries of the matrix are negative. We give a structure…

For an algebraic number $\alpha$ of degree $n$, let $\mathcal{M}_{\alpha}$ be the $\mathbb{Z}$-module generated by $1,\alpha ,\ldots ,\alpha^{n-1}$; then $\mathbb{Z}_{\alpha}:=\{\xi\in\mathbb{Q} (\alpha ):\,…

In this article we study the extent to which an $n$-dimensional compact flat manifold with the cyclic holonomy group of square-free order may be distinguished by the finite quotients of its fundamental group. In particular, we display a…

Let $\Gamma^{n}$ be the cone of an $(n-1)$-complete algebra over an algebraically closed field $k$. In this paper, we prove that if the bound quiver $(Q_{n},\rho_{n})$ of $\Gamma^{n}$ is a truncation from the bound McKay quiver…

We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the…

For a space $X$ let $\mathcal{K}(X)$ be the set of compact subsets of $X$ ordered by inclusion. A map $\phi:\mathcal{K}(X) \to \mathcal{K}(Y)$ is a relative Tukey quotient if it carries compact covers to compact covers. When there is such a…

In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants which separates the orbits. Although separating algebras are often better behaved than the ring of invariants, we show that many of the criteria…

In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in \'etale algebras. We provide a bound for the type, and give formulas to compute it. We relate the type of the overorders of a given order to the size of…

Let $G$ be a finite group and $(K,\mathcal{O},k)$ be a $p$-modular system "large enough". Let $R=\mathcal{O}$ or $k$. There is a bijection between the blocks of the group algebra $RG$ and the central primitive idempotents (the blocks) of…

Certain vertex operator algebras have integral forms (integral spans of bases which are closed under the countable set of products). It is unclear when they (or integral multiples of them) are integral as lattices under the natural bilinear…

The absolute order is a natural partial order on a Coxeter group W. It can be viewed as an analogue of the weak order on W in which the role of the generating set of simple reflections in W is played by the set of all reflections in W. By…

We study orbifolds of ${\cal N} = 4$ U(n) super-Yang-Mills theory given by discrete subgroups of SU(2) and SU(3). We have reached many interesting observations that have graph-theoretic interpretations. For the subgroups of SU(2), we have…

We study cocycle twists of a 4-dimensional Sklyanin algebra $A$ and a factor ring $B$ which is a twisted homogeneous coordinate ring. Twisting such algebras by the Klein four-group $G$, we show that the twists $A^{G,\mu}$ and $B^{G,\mu}$…

In this paper, we study finiteness criteria for the Gorenstein homological dimension of groups over a commutative ring of finite Gorenstein weak global dimension and provide estimates for the Gorenstein weak global dimension of group rings.…

Let $G$ be a finite group. The co-prime order graph of $G$ is the graph whose vertex set is $G$, and two distinct vertices $x,y$ are adjacent if gcd$(o(x),o(y))$ is either $1$ or a prime, where $o(x)$ and $o(y)$ are the orders of $x$ and…