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Title: Math/Algebra/Ring Theory - Nonassociative Rings and Algebras Section 17 in Dave Rusin's Mathematical Atlas.
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17: Nonassociative rings and algebras[The <b>Mathematical</b> Atlas] [Search][Subject Index][MathMap][Tour][Help!][MathMap Icon]ABOUT:[Introduction][History][Related areas][Subfields]POINTERS:[Texts][Software][Web links][Selected topics here]

17: Nonassociative rings and algebras

Introduction

Here are a few notes on nonassociative rings; associative rings aretreated in a separate section. There is along FAQ on sets with products (rings), aparticular emphasis of which is the study of division rings over thereals, including the nonassociative ones. For detailed expositoryinformation you are welcome to to peruse an on-linetextbook made freely available by a colleague.In nonassociative ring theory we widen the scope of rings to be studied.Here the general theory is much weaker, but special cases of such ringsare of key importance: Lie algebras in particular, as well as Jordan algebrasand other types.

History

Applications and related fields

[Schematic of subareas and related areas]

Subfields

17A: General nonassociative rings17B: Lie algebras, For Lie groups, see 22EXX17C: Jordan algebras (algebras, triples and pairs)17D: Other nonassociative rings and algebrasBrowse all (old) classifications for this area at the AMS.

Textbooks, reference works, and tutorials

"Reviews in Ring Theory, 1980-1984", American Mathematical Society, 1986 ISBN 0-8218-0097-3. Also available: reviews 1940-1979.Bourbaki, Nicolas, "Lie groups and Lie algebras. Chapters 1--3" Springer-Verlag, Berlin-New York, 1989. 450 pp. ISBN3-540-50218-1 MR89k:17001Chari, Vyjayanthi; Pressley, Andrew:"A guide to quantum groups",Corrected reprint of the 1994 original.Cambridge University Press, Cambridge, 1995. 651 pp. ISBN 0-521-55884-0 MR96h:17014A survey: Rittenberg, V.: "A guide to Lie superalgebras", Grouptheoretical methods in physics (Sixth Internat. Colloq., Tübingen,1977), pp. 3--21; Lecture Notes in Phys., 79, Springer, Berlin-NewYork, 1978. MR80d:17012

Software and tables

McKay, W. G.; Patera, J.; Rand, D. W., "Tables of representations of simple Lie algebras", Université de Montréal, Centre de Recherches Mathématiques, Montréal, 1990, ISBN 2-921120-06-2 [Only Vol. I, on the exceptional algebras, was published.] http://www.riaca.win.tue.nl/CAN/SystemsOverview/Special/Algebra/FELIX/

Other web sites with this focus

Preprint server (includes Quantum Algebra)Here are the AMS and Goettingen resource pages for area 17.Algebras and other algebraic information for physicists

Selected topics at this site

How do Lie groups and algebras fit in among the branches of mathematics?Comparison of semisimple, reductive, etc. for Lie algebras and groupsConstruction of octonions and related real algebrasYou can reach this page through http://www.math-atlas.org/welcome.htmlLast modified 2000/01/14 by Dave Rusin. Mail: rusin@math.niu.edu
 

Section

17

in

Dave

Rusin's

Mathematical

Atlas.

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