𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Lie Properties of the Group Algebra and the Nilpotency Class of the Group of Units

✍ Scribed by A.A Bovdi; J Kurdics

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
258 KB
Volume
212
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We describe the upper and lower Lie nilpotency index of a modular group algebra ‫ކ‬G of some metabelian group G and apply these results to determine the nilpotency class of the group of units, extending certain results of Shalev without restriction to finite groups. A characterization of modular group algebras ‫ކ‬G with group of units of class 3 is given, which was obtained by Rao and Sandling for finite groups G. ᮊ 1999 Academic Press Ž .

📜 SIMILAR VOLUMES

Discrete Cocompact Subgroups of the Four
Discrete Cocompact Subgroups of the Four-Dimensional Nilpotent Connected Lie Group and Their Group C*-Algebras
✍ Paul Milnes; Samuel Walters 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 153 KB

Let G 4 be the unique, connected, simply connected, four-dimensional, nilpotent Lie group. In this paper, the discrete cocompact subgroups H of G 4 are classified and shown to be in 1-1 correspondence with triples p 1 p 2 p 3 ∈ 3 that satisfy p 2 p 3 > 0 and a certain restriction on p 1 . The K-grou

Strength of Convergence in Duals of C*-A
Strength of Convergence in Duals of C*-Algebras and Nilpotent Lie Groups
✍ R.J. Archbold; E. Kaniuth; J. Ludwig; G. Schlichting; D.W.B. Somerset 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 284 KB

By using trace formulae, the recent concept of upper multiplicity for an irreducible representation of a C\*-algebra is linked to the earlier notion of strength of convergence in the dual of a nilpotent Lie group G. In particular, it is shown that if ? # G has finite upper multiplicity then this int

On the Cohomology of Infinite Dimensiona
On the Cohomology of Infinite Dimensional Nilpotent Lie Algebras
✍ A. Fialowski 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 289 KB

In the paper one- and two-dimensional cohomology is compared for finite and infinite nilpotent Lie algebras, with coefficients in the adjoint representation. It turns out that, because the adjoint representation is not a highest weight representation in infinite dimension, the considered cohomology

Computing Representations of a Lie Group
Computing Representations of a Lie Group via the Universal Enveloping Algebra
✍ Philip Feinsilver; René Schott 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 373 KB

We present an algorithm for the computation of representations of a Lie algebra acting on its universal enveloping algebra. This is a new algorithm which permits the effective computation of these representations and of the matrix elements of the corresponding Lie group. The approach is based on a m