REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES

We present an extremely elementary construction of the simple Lie algebras over C in all of their minuscule representations, using the vertices of various polytopes. The construction itself requires no complicated combinatorics and essentially no Lie theory other than the definition of a Lie algebra; in fact, the Lie algebras themselves appear as by-products of the construction.

Keywords:

Lie algebra, minuscule representation polytope,

Tam Metin

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Department of Mathematics University of Colorado Campus Box 395 Boulder, CO 80309-0395 USA e-mail: rmg@euclid.colorado.edu

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Bibtex	@ { ieja266373, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2008}, volume = {4}, number = {4}, pages = {27 - 52}, title = {REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES}, key = {cite}, author = {Green, Richard M.} }
APA	Green, R. M. (2008). REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES . International Electronic Journal of Algebra , 4 (4) , 27-52 .
MLA	Green, R. M. "REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES" . International Electronic Journal of Algebra 4 (2008 ): 27-52 <
Chicago	Green, R. M. "REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES". International Electronic Journal of Algebra 4 (2008 ): 27-52
RIS	TY - JOUR T1 - REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES AU - Richard M.Green Y1 - 2008 PY - 2008 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 27 EP - 52 VL - 4 IS - 4 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2022 ER -
EndNote	%0 International Electronic Journal of Algebra REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES %A Richard M. Green %T REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES %D 2008 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 4 %N 4 %R %U
ISNAD	Green, Richard M. . "REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES". International Electronic Journal of Algebra 4 / 4 (Aralık 2008): 27-52 .
AMA	Green R. M. REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES. IEJA. 2008; 4(4): 27-52.
Vancouver	Green R. M. REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES. International Electronic Journal of Algebra. 2008; 4(4): 27-52.
IEEE	R. M. Green , "REPRESENTATIONS OF LIE ALGEBRAS ARISING FROM POLYTOPES", , c. 4, sayı. 4, ss. 27-52, Ara. 2008

International Electronic Journal of Algebra

ISSN: 1306-6048
Yayın Aralığı: Yılda Aylık
Yayıncı: Abdullah HARMANCI