Related papers: More Examples of Non-Rational Adjoint Groups

The model-theoretic Grothendieck ring of a first order structure, as defined by Krajic\v{e}k and Scanlon, captures some combinatorial properties of the definable subsets of finite powers of the structure. In this paper we compute the…

A very useful fact in additive combinatorics is that analytic expressions that can be used to count the number of structures of various kinds in subsets of Abelian groups are robust under quasirandom perturbations, and moreover that…

We introduce a new method to study rational conjugacy of torsion units in integral group rings using integral and modular representation theory. Employing this new method, we verify the first Zassenhaus Conjecture for the group…

Let $E$ be a elementary abelian $p$-group of order $q=p^n$. Let $W$ be a faithful indecomposable representation of $E$ with dimension 2 over a field $k$ of characteristic $p$, and let $V= S^m(W)$ with $m<q$. We prove that the rings of…

It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the coefficients entering Kontsevich's formality quasi-isomorphism arXiv:q-alg/9709040, there are irrational (possibly even transcendental) numbers. In this paper, we prove that…

For G an almost simple simply connected algebraic group defined over a field F, Rost has shown that there exists a canonical map R_G: H^1(F, G) --> H^3(F, Q/Z(2)). This includes the Arason invariant for quadratic forms and Rost's mod 3…

Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…

In this paper, we study the non trivial idempotents of the $2 \times 2$ matrix ring over the polynomial ring $\mathbb{Z}_{pqr}[x]$ for distinct primes $p, q $ and $r$ greater than $3$. We have classified all the idempotents of this matrix…

Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed…

In this paper, we consider a one-parameter family of degree $d\ge 2$ rational maps with an automorphism group containing the cyclic group of order $d$. We construct a polynomial whose roots correspond to parameter values for which the…

In the present paper we study stability of recurrence equations (which in particular case contain a dynamics of rational functions) generated by contractive functions defined on an arbitrary non-Archimedean algebra. Moreover,…

We study a family of Calabi--Yau algebras that include the quadratic Artin--Schelter regular algebras associated to a nodal cubic. It is shown that these algebras have trivial ozone group, that is, the identity is the only automorphism that…

A conjecture of Benjamini & Schramm from 1996 states that any finitely generated group that is not a finite extension of Z has a non-trivial percolation phase. Our main results prove this conjecture for certain groups, and in particular…

For an odd quadratic space $V$ of Witt index $\geq 3$ over a commutative ring with pseudoinvolution, we classify the subgroups of the odd unitary group $U(V)$ that are normalized by the elementary subgroup $EU_{(e_1,e_{-1})}(V)$ defined by…

We compute the genus of a rational quadratic form in terms of the K-theory of a C*-algebra attached to the adelic orthogonal group of the form. As a corollary, one gets a higher composition law for the rational quadratic forms. As an…

Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups $SU(2)$ and $SU(1,1)$…

In this article, we construct partial periodic quotients of groups which have a non-elementary acylindrical action on a hyperbolic space. In particular, we provide infinite quotients of mapping class groups where a fixed power of every…

The multivariate quantum $q$-Krawtchouk polynomials are shown to arise as matrix elements of "$q$-rotations" acting on the state vectors of many $q$-oscillators. The focus is put on the two-variable case. The algebraic interpretation is…

We give a closed formula for the number of partitions $\lambda$ of $n$ such that the corresponding irreducible representation $V_\lambda$ of $S_n$ has non-trivial determinant. We determine how many of these partitions are self-conjugate and…

Let R be a Noetherian commutative ring of dimension n >2 and let A=R[T,T^{-1}]. Assume that the height of the Jacobson radical of R is atleast 2. Let P be a projective A-module of rank n=dim A - 1 with trivial determinant. We define an…