Related papers: Automorphisms of modular lattices

We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We…

We show that if L is an extremal even unimodular lattice of rank 40r with r=1,2,3 then L is generated by its vectors of norms 4r and 4r+2. Our result is an extension of Ozeki's result for the case r=1.

In this paper we compare the $\mathbb J$-stratification (or the semi-module stratification) and the Ekedahl-Oort stratification of affine Deligne-Lusztig varieties in the superbasic case. In particular, we classify the cases where the…

We classify one-dimensional restricted central extensions of the modular Witt Lie algebra in characteristic $p>3$.

We prove an automatic convergence theorem for holomorphic modular forms on tube domains. The argument works in some generality, and covers in particular the case of orthogonal groups, symplectic groups, unitary and quaternion unitary…

We investigate the complexity of the partial order relation of Young's lattice. The definable relations are characterized by establishing the maximal definability property modulo the single automorphism given by conjugation; consequently,…

The author determines the structure of automorphism groups of smooth plane curves of degree at least four. Furthermore, he gives some upper bounds for the order of automorphism groups of smooth plane curves and classifies the cases with…

We classify the symplectic automorphism groups for cubic fourfolds. The main inputs are the global Torelli theorem for cubic fourfolds and the classification of the fixed-point sublattices of the Leech lattice. Among the highlights of our…

In this paper, we study moduli spaces of low dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of…

We describe the moduli spaces of morphisms between polarized complex abelian varieties. The discrete invariants, derived from a Poincare' decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in…

The lattice vertex operator algebra $V_L$ associated to a positive definite even lattice $L$ has an automorphism of order 2 lifted from -1-isometry of $L$. We prove that for the fixed point vertex operator algebra $V_L^+$, any…

The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…

Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of $M.$ For type I von Neumann algebras $E(M)$ coincides with the algebra $LS(M)$ of all locally measurable operators affiliated with $M.$ In this case we show that an…

Using a description of the cohomology of local systems on the moduli space of abelian surfaces with a full level two structure, together with a computation of Euler characteristics we find the isotypical decomposition, under the symmetric…

In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.

Let $\mathcal{F}$ denote a singular holomorphic foliation on $\mathbb{P}^2$ having a finite automorphism group $\mbox{aut}(\mathcal{F})$. Fixed the degree of $\mathcal{F}$, we determine the maximal value that $|\mbox{aut}(\mathcal{F})|$ can…

Let $L$ be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of $L$ contained in the center of $L$ and endomorphisms $j$ of $L$ satisfying the Borceux-Van den Bossche conditions.

Firstly, we give a partial solution to the isomorphism problem for uniserial modules of finite length with the help of the morphisms between these modules over an arbitrary ring. Later, under suitable assumptions on the lattice of the…

The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…