## Algebres EnveloppantesThis is an English edition of Dixmier's book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Dixmier was awarded the Leroy P. Steele prize for expository writing in mathematics. The Committee's citation described this as one of Dixmier's extraordinary books. Written with unique precision and elegance, the book provides the reader with insight and understanding of this very important subject. It can be an excellent textbook for a graduate course, as well as a very useful source of references in the theory of universal enveloping algebras, the area of mathematics that remains as important today as it was 20 years ago. For the 1996 edition the author updated the status of open problems and added some relevant references. |

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THE DIXMIER MAP FOR CERTAIN ENVELOPING ALGEBRAS this action. Our **...**

M. LORENZ, 'Chains of prime ideals in enveloping algebras of solvable Lie algebras', J. London Math. Soc. (2), 24 (1981), 205-210. ...

blms.oxfordjournals.org/ cgi/ reprint/ 14/ 5/ 403.pdf

JSTOR: Kmax and Stable Rank of Enveloping Algebras

In this paper we consider the stable rank and Kmax of enveloping algebras of many nonabelian solvable Lie algebras, including all nonabelian nilpotent Lie ...

links.jstor.org/ sici?sici=0002-9939(199311)119%3A3%3C691%3AKASROE%3E2.0.CO%3B2-C

Universal enveloping algebra - Wikipedia, the free encyclopedia

As mentioned above, the construction of universal enveloping algebras is part ... Furthermore, both group algebras and universal enveloping algebras carry ...

en.wikipedia.org/ wiki/ Universal_enveloping_algebra

SOME NORMS ON UNIVERSAL ENVELOPING ALGEBRAS

universal enveloping algebras on the other is isometric with respect to certain natural. norms on the universal enveloping algebras. ...

journals.cms.math.ca/ cgi-bin/ vault/ public/ view/ gross0699/ body/ PDF/ gross0699.pdf?file=gross0699

Formality and Deformations of Universal Enveloping Algebras

Abstract We describe enveloping algebras of finite-dimensional Lie ... For instance, the universal enveloping algebras of the Lie algebras gl(n,K) ⊕ K ...

www.springerlink.com/ index/ 42w26ml594256t4r.pdf

Sheets and hearts of prime ideals in enveloping algebras of **...**

General notations, especially concerning enveloping algebras ... Sometimes we shall work with enveloping algebras over a base field extension K of the ...

linkinghub.elsevier.com/ retrieve/ pii/ S0021869306000858

ON SUPPORTS AND ASSOCIATED PRIMES OF MODULES OVER THE ENVELOPING **...**

OF MODULES OVER THE ENVELOPING ALGEBRAS. OF NILPOTENT LIE ALGEBRAS. BORISSIROLA. Abstract. Let n be a nilpotent Lie algebra, over a field of characteristic ...

www.ams.org/ tran/ 2001-353-06/ S0002-9947-01-02741-6/ S0002-9947-01-02741-6.pdf

Borho, Brylinski: Differential operators on homogeneous spaces. II **...**

Our main object here is to analyse the process of induction of (two-sided) ideals in enveloping algebras, in particular the behaviour of their associated ...

www.numdam.org/ numdam-bin/ fitem?id=BSMF_1989__117_2_167_0

Springer Online Reference Works

The twisted induction on the level of enveloping algebras corresponds to the ... It is known that for enveloping algebras of Lie algebras, left and right ...

eom.springer.de/ d/ d120240.htm

Hopf Structure for Poisson Enveloping Algebras

[1] Dixmier, J.: Enveloping algebras. The 1996 printing of the 1977 English translation Grad- ... [4] Oh, Sei-Qwon: Poisson enveloping algebras. Comm. ...

www.emis.de/ journals/ BAG/ vol.44/ no.2/ b44h2sqo.pdf