Related papers: Hyper-Reinhardt Free Spectrahedra
We describe the groups of automorphisms of two generated free braided associative algebras with involutive diagonal braidings over a field of characteristic $\neq 2$. Depending on the form of the diagonal involutive braiding, five different…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
In the past two decades, extensive research has been conducted on the (co)homology of various models of random simplicial complexes. So far, it has always been examined merely as a list of groups. This paper expands upon this by describing…
If $f$ is an automorphism of a compact simply connected K\"ahler manifold with trivial canonical bundle that fixes a K\"ahler class, then the order of $f$ is finite. We apply this well known result to construct compact non-K\"ahler…
We prove that a "random" free group outer automorphism is an ageometric fully irreducible outer automorphism whose ideal Whitehead graph is a union of triangles. In particular, we show that its attracting (and repelling) tree is a…
The operation of switching a graph $\Gamma$ with respect to a subset $X$ of the vertex set interchanges edges and non-edges between $X$ and its complement, leaving the rest of the graph unchanged. This is an equivalence relation on the set…
We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived…
Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in…
It is known that the automorphism group of any projective K3 surface is finitely generated [24]. In this paper, we consider a certain kind of K3 surfaces with Picard number 3 whose automorphism groups are isomorphic to congruence subgroups…
We consider the entanglement properties of free fermions in one dimension and review an approach which relates the problem to the solution of a certain differential equation. The single-particle eigenfunctions of the entanglement…
We study endomorphisms of a free group of finite rank by means of their action on specific sets of elements. In particular, we prove that every endomorphism of the free group of rank 2 which preserves an automorphic orbit (i.e., acts ``like…
We observe that the singular part of the second bounded cohomology group of boundedly simple groups is trivial.
An automorphism of an algebraic surface $S$ is called cohomologically (numerically) trivial if it acts identically on the second $l$-adic cohomology group (this group modulo torsion subgroup). Extending the results of S. Mukai and Y.…
We show that real second order freeness appears in the study of Haar unitary and unitarily invariant random matrices when transposes are also considered. In particular we obtain the unexpected result that a unitarily invariant random matrix…
Let \sigma be an automorphism of a commutative k-algebra R. The skew polynomial ring R[t;\sigma] is generated by R and an indeterminate t subject to the relations ta=\sigma(a)t for all a in R. For certain R and appropriate \sigma there are…
We prove that the group of automorphisms of the category of free modules over Noterian rings is semi-inner and present also a short proof of a similar result for the variery of Lie algebras.
Let $R$ be a real smooth affine domain of dimension $3$ such that $R$ has either no real maximal ideals or the intersection of all real maximal ideals in $R$ has height at least $1$. Then we prove that all stably free $R$-modules of rank…
A classification of discrete polymatroids whose independence polytopes are reflexive will be presented.
We consider the infinite-dimensional hypercube graph. This graph is not connected and has isomorphic connected components. We describe the restrictions of its automorphisms to the connected components and the automorphism group of connected…
We prove that the group of tame automorphisms of a free Lie algebra (as well as of a free anticommutative algebra) rank 3 over an arbitrary integral domain has the structure of an amalgamated free product. We construct an example of a wild…