Related papers: Brauer equivalent number fields and the geometry o…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
In this paper, we discuss O-basis of symmetry classes of polynomials associated with the Brauer character of the Semi-Dihedral groups and Dihedral groups. Also, necessary and sufficient conditions are given for the existence of an…
We introduce the periplectic $q$-Brauer category over an integral domain of characteristic not $2$. This is a strict monoidal supercategory and can be considered as a $q$-analogue of the periplectic Brauer category. We prove that the…
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics…
In this paper, we give an equivalent condition for an abelian variety over a finite field to have multiplication by a quaternion algebra over a number field. We prove the result by combining Tate's classification of the endomorphism…
In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…
The unconstrained frame-like formulation of an infinite tower of completely symmetric tensor gauge fields is reviewed and examined in the limit where the cosmological constant goes to zero. By partially fixing the gauge and solving the…
We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity. We show that these conditions are directly related to important conjectures in number theory coming from…
Two Azumaya algebras with involutions are considered over a regular local ring. It is proved that if they are isomorphic over the quotient field, then they are isomorphic too. In particular, if two quadratic spaces over such a ring are…
We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of…
Two metrics $g $ and $\bar g$ are geodesically equivalent, if they share the same (unparameterized) geodesics. We introduce two constructions that allow one to reduce many natural problems related to geodesically equivalent metrics, such as…
In this paper after proving (in Section 2) the Berkovich analytic space analog of the familiar fact that there exist many non-isomorphic Riemann surfaces of the fixed topological type, I introduce the precise notion of Arithmetic…
We classify the algebraic combinatorial geometries of arbitrary field extensions of transcendence degree greater than 4 and describe their groups of automorphisms. Our results and proofs extend similar results and proofs by Evans and…
After introducing the different boundary geometries of rank one symmetric spaces, we state and prove Fried's theorem in the general setting of all those geometries: a closed manifold with a similarity structure is either complete or the…
In this paper, we give a necessary and sufficient condition for a cyclotomic Brauer algebra being semisimple. This generalizes previous result for a Brauer algebra.
In this article, we compare the cohomology between the categories of modules of the diagram algebras and the categories of modules of its input algebras. Our main result establishes a sufficient condition for exact split pairs between these…
Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…
In this paper we develop techniques for computing the relative Brauer group of curves, focusing particularly on the case where the genus is 1. We use these techniques to show that the relative Brauer group may be infinite (for certain…
We characterise when there exists a quasiisometric embedding between two solvable Baumslag-Solitar groups. This extends the work of Farb and Mosher on quasiisometries between the same groups. More generally, we characterise when there can…
We show that two well-studied classes of tame algebras coincide: namely, the class of symmetric special biserial algebras coincides with the class of Brauer graph algebras. We then explore the connection between gentle algebras and…