Search results for "algebra"

On a problem of P. Hall for Engel words

2011

Conjugately dense subgroups in generalized $FC$-groups

2009

ALGEBRE SIMMETRICHE DI ALCUNE CLASSI DI IDEALI MONOMIALI

The purpose of this thesis is the study of the symmetric algebra 〖Sym〗_S (L) of an interesting class of monomial ideals: the ideals L ⊂S=K[x1,...,xn,y1,...,ym] of mixed products in two sets of variables. Recently, this class is been used in order to test some algebraic conjecture, including the conjecture of Eisenbud -Goto, on the symmetric algebra 〖Sym〗_S (L) .Since such conjecture involves fundamental invariants of Sym (L), such as the Krull dimension, the multiplicity and regularity of Castelnuovo-Mumford, it was necessary to calculate these invariants or their bounds. This problem is difficult, but if L is generated by a s-sequence, you can arrive at a concrete result. In the work Mixed…

The ziqqurath of exact sequences of n-groupoids

2011

In this work we study exactness in the sesqui-category of n-groupoids. Using homotopy pullbacks, we construct a six term sequence of (n-1)-groupoids from an n-functor between pointed n-groupoids. We show that the sequence is exact in a suitable sense, which generalizes the usual notions of exactness for groups and categorical groups. Moreover, iterating the process, we get a ziqqurath of exact sequences of increasing length and decreasing dimension. For n = 1 we recover a classical result due to R. Brown and, for n = 2 its generalizations due to Hardie, Kamps and Kieboom and to Duskin, Kieboom and Vitale.

On a result of L.-C. Kappe and M. Newell

2009

There is a long line of research investigating upper central series of a group. The interest comes from the information which these series can give on the structure of a group. Baer (1952) extended the usual notion of center of a group, introducing that of p-centre, where p is a prime. Almost 40 years later, Kappe and Newell (1989) were able to embed the p-centre of a metabelian p-group in the p-th term of the upper central series. This was possible because of the growing knowledge on Engel groups of the 60s years. Here we extend the result of Kappe and Newell (1989) to wider classes of groups.

On the asymptotics for $ast$-Capelli identities

Let Fbe the free associative algebra with involution ∗ over a field of characteristic zero. If L and M are two natural numbers let Γ∗_M+1,L+1 denote theT∗-idealofFgenerated by the∗-capellipolynomialsCap+M+1,Cap−L+1 alternanting on M+1 symmetric variables and L+1skew variables,respectively.It is well known that, if F is an algebraic closed field, every finite dimensional ∗-simple algebra is isomorphic to one of the following algebras (see [4], [2]):· (Mk(F),t) with the transpose involution; · (M2m(F),s) with the symplectic involution; · (Mk(F)⊕Mk(F)op,∗) with the exchange involution. The aim of this talk is to show a relation among the asymptotics of the∗-codimensions of the finite dimensional ∗…

Varieties of algebras of polynomial growth

2008

Let V be a proper variety of associative algebras over a field F of characteristic zero. It is well-known that V can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of var(G) and var(UT 2), where G is the Grassmann algebra and UT2 is the algebra of 2 x 2 upper triangular matrices.

A note on strong protomodularity, actions and quotients

2013

We investigate some properties of the fibration of points. We obtain a characterization of protomodular categories among pointed regular ones, and, in the semi-abelian case, a characterization of strong protomodularity. Everything is also stated in terms of internal actions.

Wielandt's results for algebraic k-groups

2006

We analyze the relation between subnormality and nilpotence, the subnormal joint property, some criteria of subnormality, the norm and the Wielandt subgroup in the case of algebraic groups defined over an arbitrary field.

Algebraic Geometry between Tradition and Future

2023

An incredible season for algebraic geometry flourished in Italy between 1860, when Luigi Cremona was assigned the chair of Geometria Superiore in Bologna, and 1959, when Francesco Severi published the last volume of the treatise on algebraic systems over a surface and an algebraic variety. This century-long season has had a prominent influence on the evolution of complex algebraic geometry - both at the national and international levels - and still inspires modern research in the area. "Algebraic geometry in Italy between tradition and future" is a collection of contributions aiming at presenting some of these powerful ideas and their connection to contemporary and, if possible, future deve…