Search results for "mutation."
showing 10 items of 2808 documents
Central Units, Class Sums and Characters of the Symmetric Group
2010
In the search for central units of a group algebra, we look at the class sums of the group algebra of the symmetric group S n in characteristic zero, and we show that they are units in very special instances.
Group algebras whose units satisfy a group identity
1997
Let F G FG be the group algebra of a torsion group over an infinite field F F . Let U U be the group of units of F G FG . We prove that if U U satisfies a group identity, then F G FG satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.
The complex of words and Nakaoka stability
2005
We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position". Hm(§ni1;Z) = Hm(§n;Z) for n=2 > m where §n denotes the permutation group of n elements. An elementary proof of this fact has not been available in the literature. In the first section the complex C⁄(m) of abelian groups is studied which in de- gree n is freely generated by injective words of length n. The alphabet consists of m letters. The complex C⁄(m) has the only non vanishing homology in degree m (Theorem 1). This is a result of F.…
Asymptotics for the standard and the Capelli identities
2003
Let {c n (St k )} and {c n (C k )} be the sequences of codimensions of the T-ideals generated by the standard polynomial of degreek and by thek-th Capelli polynomial, respectively. We study the asymptotic behaviour of these two sequences over a fieldF of characteristic zero. For the standard polynomial, among other results, we show that the following asymptotic equalities hold: $$\begin{gathered} c_n \left( {St_{2k} } \right) \simeq c_n \left( {C_{k^2 + 1} } \right) \simeq c_n \left( {M_k \left( F \right)} \right), \hfill \\ c_n \left( {St_{2k + 1} } \right) \simeq c_n \left( {M_{k \times 2k} \left( F \right) \oplus M_{2k \times k} \left( F \right)} \right), \hfill \\ \end{gathered} $$ wher…
Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2
1996
Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.
Quantum Queries on Permutations
2015
K. Iwama and R. Freivalds considered query algorithms where the black box contains a permutation. Since then several authors have compared quantum and deterministic query algorithms for permutations. It turns out that the case of \(n\)-permutations where \(n\) is an odd number is difficult. There was no example of a permutation problem where quantization can save half of the queries for \((2m+1)\)-permutations if \(m\ge 2\). Even for \((2m)\)-permutations with \(m\ge 2\), the best proved advantage of quantum query algorithms is the result by Iwama/Freivalds where the quantum query complexity is \(m\) but the deterministic query complexity is \((2m-1)\). We present a group of \(5\)-permutati…
The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation
2021
We describe the left brace structure of the structure group and the permutation group associated to an involutive, non-degenerate set-theoretic solution of the quantum YangBaxter equation by using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.
Transitive permutation groups in which all derangements are involutions
2006
AbstractLet G be a transitive permutation group in which all derangements are involutions. We prove that G is either an elementary abelian 2-group or is a Frobenius group having an elementary abelian 2-group as kernel. We also consider the analogous problem for abstract groups, and we classify groups G with a proper subgroup H such that every element of G not conjugate to an element of H is an involution.
On permutations of class sums of alternating groups
1997
We prove a result concerning the class sums of the alternating group An; as a consequence we deduce that if θ is a normalized automorphism of the integral group ring then there exists such that is the identity on , where Sn:is the symmetric group and is the center of
Weak commutation relations of unbounded operators and applications
2011
Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.