Search results for " Algebra"
showing 10 items of 2082 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.
Hypergraph functor and attachment
2010
Using an arbitrary variety of algebras, the paper introduces a fuzzified version of the notion of attachment in a complete lattice of Guido, to provide a common framework for the concept of hypergraph functor considered by different authors in the literature. The new notion also gives rise to a category of variable-basis topological spaces which is a proper supercategory of the respective category of Rodabaugh.
Group-graded algebras with polynomial identity
1998
LetG be a finite group and letR=Σg∈GRg be any associative algebra over a field such that the subspacesRg satisfyRgRh⊆Rgh. We prove that ifR1 satisfies a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the order ofG. This result implies the following: ifH is a finite-dimensional semisimple commutative Hopfalgebra andR is anyH-module algebra withRH satisfying a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the dimension ofH.
On Join Properties of Hall π-Subgroups of Finite π-Soluble Groups
1998
All groups considered in the sequel are finite. K. Doerk and T. Hawkes, in Section I.4 of their recent comprehensive w x volume on finite soluble groups 1 , include background material and a proof of the following result: Let S be a Hall system of a soluble group G and let U and V be subgroups into which S reduces. Then S reduces into U l V, and if , in addition, U permutes with V, then S reduces into UV. It is clear that the second part of the above result holds equally well with a single Hall subgroup in place of a Hall system; in other words, if a Hall p-subgroup of G contains Hall p-subgroups of U and V and U permutes with V, then it also contains a Hall p-subgroup of UV.
A Star-Variety With Almost Polynomial Growth
2000
Abstract Let F be a field of characteristic zero. In this paper we construct a finite dimensional F -algebra with involution M and we study its ∗ -polynomial identities; on one hand we determine a generator of the corresponding T -ideal of the free algebra with involution and on the other we give a complete description of the multilinear ∗ -identities through the representation theory of the hyperoctahedral group. As an outcome of this study we show that the ∗ -variety generated by M , var( M , ∗ ) has almost polynomial growth, i.e., the sequence of ∗ -codimensions of M cannot be bounded by any polynomial function but any proper ∗ -subvariety of var( M , ∗ ) has polynomial growth. If G 2 is…
Towards Vorst's conjecture in positive characteristic
2018
Vorst's conjecture relates the regularity of a ring with the $\mathbb{A}^1$-homotopy invariance of its $K$-theory. We show a variant of this conjecture in positive characteristic.
Exponential Codimension Growth of PI Algebras: An Exact Estimate
1999
Abstract LetAbe an associative PI-algebra over a fieldFof characteristic zero. By studying the exponential behavior of the sequence of codimensions {cn(A)} ofA, we prove thatInv(A)=limn→∞ c n ( A ) always exists and is an integer. We also give an explicit way for computing such integer: letBbe a finite dimensionalZ2-graded algebra whose Grassmann envelopeG(B) satisfies the same identities ofA; thenInv(A)=Inv(G(B))=dim C(0)+dim C(1)whereC(0)+C(1)is a suitableZ2-graded semisimple subalgebra ofB.
Séparation des orbites coadjointes d'un groupe exponentiel par leur enveloppe convexe
2008
Resume Revenant sur la question de la separation des representations unitaires irreductibles d'un groupe de Lie exponentiel G par leur application moment, nous presentons ici une nouvelle solution : au lieu de prolonger l'application moment a l'algebre enveloppante de G , nous proposons de definir une application (non lineaire) Φ de g ∗ dans le dual g + ∗ de l'algebre de Lie d'un groupe resoluble G + , de prolonger les representations de G a G + de telle facon que les orbites coadjointes correspondantes de G + soient caracterisees par l'adherence de leur enveloppe convexe. Ceci nous permet de separer les representations irreductibles de G .
Topological lower bounds on the distance between area preserving diffeomorphisms
2000
Area preserving diffeomorphisms of the 2-disk which are Identity near the boundary form a group which can be equipped, using theL2-norm on its Lie algebra, with a right invariant metric. In this paper we give a lower bound on the distance between diffeomorphisms which is invariant under area preserving changes of coordinates and which improves the lower bound induced by the Calabi invariant. In the case of renormalizable and infinitely renormalizable maps, our estimate can be improved and computed.
The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group
2000
It was conjectured by Tits that the only relations amongst the squares of the standard generators of an Artin group are the obvious ones, namely that a^2 and b^2 commute if ab=ba appears as one of the Artin relations. In this paper we prove Tits' conjecture for all Artin groups. More generally, we show that, given a number m(s)>1 for each Artin generator s, the only relations amongst the powers s^m(s) of the generators are that a^m(a) and b^m(b) commute if ab=ba appears amongst the Artin relations.