Related papers: Linear Algebra Estimates

Let $\alpha$, $\beta$, and $\gamma$ be partitions describing the isomorphism types of the finite abelian $p$-groups $A$, $B$, and $C$. From theorems by Green and Klein it is well-known that there is a short exact sequence $0\to A\to B\to…

There is a polymodal provability logic $GLP$. We consider generalizations of this logic: the logics $GLP_{\alpha}$, where $\alpha$ ranges over linear ordered sets and play the role of the set of indexes of modalities. We consider the…

If $A$ is a subset of the set of reflections of a finite Coxeter group $W$, we define a sub-${\mathbb{Z}}$-module ${\mathcal{D}}_A(W)$ of the group algebra ${\mathbb{Z}} W$. We provide examples where this submodule is a subalgebra. This…

Poisson-Lie T-duality/plurality was recently generalized to Jacobi-Lie T-plurality formulated in terms of Double Field Theory and based on Leibniz algebras given by structure coefficients $f_{ab}{}^{c},f_{c}{}^{ab},$ and $Z_a,Z^a$. We…

In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by…

Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is…

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…

Let $\mathcal{Z}(\mathcal{U}(\mathbb{Z}[G]))$ denote the group of central units in the integral group ring $\mathbb{Z}[G]$ of a finite group $G$. A bound on the index of the subgroup generated by a virtual basis in…

Let W_n(K) be the Lie algebra of derivations of the polynomial algebra K[X]:=K[x_1,...,x_n] over an algebraically closed field K of characteristic zero. A subalgebra L of W_n(K) is called polynomial if it is a submodule of the K[X]-module…

We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…

The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic…

It is an important result of \v Semrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for…

We show that elementary abelian direct factors can be disregarded in the study of the modular isomorphism problem. Moreover, we obtain four new series of abelian invariants of the group base in the modular group algebra of a finite…

Let L be a countable elementary language, N be a Fraisse limit. We consider free amalgamation for L-structures where L is arbitrary. If free amalgamation for finitely generated substructures exits in N, then it is a stationary independece…

Let $p$ be a prime and let $G$ be a finite $p$-group. We show that the isomorphism type of the maximal abelian direct factor of $G$, as well as the isomorphism type of the group algebra over $\mathbb F_p$ of the non-abelian remaining direct…

The concept of Automorphic Lie Algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. Automorphic Lie Algebras are obtained by imposing a discrete group symmetry on a current…

Let $X$ be a finitely generated left module over a left artinian ring $R$, and let $p(X)=\{l_i\}$ be the infinite sequence of nonnegative integers where $l_i$ is the length of the $i$-th term of the minimal projective resolution of $X$. We…

We define algebraic cobordism of classifying spaces, \Omega^*(BG) and G-equivariant algebraic cobordism \Omega^*_G(-) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted…

In the setting of product systems over group-embeddable monoids, we consider nuclearity of the associated Toeplitz C*-algebra in relation to nuclearity of the coefficient algebra. Our work goes beyond the known cases of single…

A linear group is called unisingular if every element of it has eigenvalue 1. A certain aspect of the theory of abelian varieties requires the knowledge of unisingular irreducible subgroups of the symplectic groups over the field of two…