𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Lifting Theorem with Applications to Blocks and Source Algebras

✍ Scribed by Burkhard Külshammer; Tetsuro Okuyama; Atumi Watanabe

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
100 KB
Volume
232
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

The main purpose of this paper is to present a lifting theorem generalizing the well-known Wedderburn᎐Malcev theorem. We then show how this result can be applied to various questions concerning the structure of blocks and source algebras. In particular, we indicate how it can be used to give an alternative proof of Puig's main theorem on nilpotent blocks.

In the following, we fix a complete discrete valuation ring R with Ž . algebraically closed residue field F s RrJ R of characteristic p ) 0 and field of fractions K of characteristic 0. For an element ␣ g R, we denote by ␣ its image in F. All our R-algebras will be associative with identity element and finitely generated R-modules. We do not require our R-algebra homomorphisms to be unitary.

Let us fix an R-algebra A. Every A-module will be considered as an R-module in the usual way. We will tacitly assume that all our A-bimodules M satisfy rm s mr for r g R, m g M. Then we can regard A Ä 4

M [ m g M : am s ma for a g A

📜 SIMILAR VOLUMES

A Six Generalized Squares Theorem, with
A Six Generalized Squares Theorem, with Applications to Polynomial Identity Algebras
✍ Paula B. Cohen; Amitai Regev 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 113 KB

The theories of superalgebras and of P.I. algebras lead to a natural ‫ޚ‬ -graded 2 extension of the integers. For these generalized integers, a ''six generalized squares'' theorem is proved, which can be considered as a ‫ޚ‬ -graded analogue of 2 the classical ''four squares'' theorem for the natural

A central limit theorem with application
A central limit theorem with applications to random hypergraphs
✍ Peter de Jong 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 691 KB

Define for each subset I C (1,. . . , n} the c+-algebra 9, = m{X, : i E I} with X , , . . . , X , independent random variables. In this paper we consider 9,measurable random variables W, subject to the centering condition E(W, I 9,) = 0 a s .