𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Irreducible Finitary Lie Algebras over Fields of Characteristic Zero

✍ Scribed by Felix Leinen; Orazio Puglisi

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
67 KB
Volume
210
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

‫ދ‬

finite rank. We show that if Char ‫ދ‬ s 0, if dim V is infinite, and if L acts ‫ދ‬ irreducibly on V, then the derived algebra of L is simple. ᮊ 1998 Academic Press Let V be a vector space over the field ‫.ދ‬ The endomorphisms of finite Ž . rank form an ideal in End V , which becomes a locally finite Lie algebra ‫ދ‬ w

x Ž w x . with respect to the usual Lie bracket a, b s ab y ba see 11, p. 32 . We Ž . shall denote this Lie algebra by ᒃ ᒄ ᒉ V . A Lie algebra L is said to be ‫ދ‬ finitary if there exist a field ‫ދ‬ and a ‫-ދ‬vector space V such that L is Ž . isomorphic to a subalgebra of ᒃ ᒄ ᒉ V .

‫ދ‬

The study of finitary Lie algebras is motivated, in part, by the wealth of Ž . results available about finitary linear groups, i.e., subgroups of GL V ‫ދ‬ consisting of elements g such that the endomorphism g y 1 has finite Ž w x. w x rank see 10 . In 8 we have shown that nontrivial ascending subalgebras of infinite-dimensional irreducible finitary Lie algebras are themselves w x irreducible. It was therefore conjectured in 8 that infinite-dimensional 697

📜 SIMILAR VOLUMES

Commuting Varieties of Lie Algebras over
Commuting Varieties of Lie Algebras over Fields of Prime Characteristic
✍ Paul Levy 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 117 KB

Let K be an algebraically closed field of positive characteristic and let G be a reductive group over K with Lie algebra . This paper will show that under certain mild assumptions on G, the commuting variety is an irreducible algebraic variety.  2002 Elsevier Science (USA)

New Generalized Simple Lie Algebras of C
New Generalized Simple Lie Algebras of Cartan Type over a Field with Characteristic 0
✍ Xiaoping Xu 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 239 KB

We construct four new series of generalized simple Lie algebras of Cartan type, using the mixtures of grading operators and down-grading operators. Our results in this paper are further generalizations of those in Osborn's work (J. Algebra 185 (1996), 820-835).

The Distribution of Zeros of an Irreduci
The Distribution of Zeros of an Irreducible Curve over a Finite Field
✍ Zhiyong Zheng 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 473 KB

Let f (x, y) be a polynomial defined over Z in two variables of total degree d 2, and let Vp=[(x, y) # C p : f(x, y)#0 (mod p)] for each prime p, where C p = [(x, y) # Z 2 : 0 x<p and 0 y<p]. In this paper, we show that if f (x, y) is absolutely irreducible modulo p for all sufficiently large p, the

E-Algebraic Functions over Fields of Pos
E-Algebraic Functions over Fields of Positive Characteristic—An Analogue of Differentially Algebraic Functions
✍ Habib Sharif 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 158 KB

A function or a power series f is called differentially algebraic if it satisfies a Ž X Ž n. . differential equation of the form P x, y, y , . . . , y s 0, where P is a nontrivial polynomial. This notion is usually defined only over fields of characteristic zero and is not so significant over fields