publication . Preprint . Article . 2013

Locally Finite Root Supersystems

Malihe Yousofzadeh;
Open Access English
  • Published: 31 Aug 2013
Abstract
ABSTRACTWe introduce the notion of locally finite root supersystems as a generalization of both locally finite root systems and generalized root systems. We classify irreducible locally finite root supersystems.
Subjects
free text keywords: Mathematics - Quantum Algebra, Mathematics - Representation Theory, 17B22, 17B65, Root system, Algebra, Mathematics
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17 references, page 1 of 2

[1] S. Azam, H. Yamane and M. Yousofzadeh, Reflectable bases for affine reflection systems, J. Algebra 371 (2012) 63-93.

[2] B.N. Allison, G. Benkart and Y. Gao, Lie algebras graded by the root systems BCr, r ≥ 2, Mem. Amer. Math. Soc. 158 (2002), no. 751, x+158.

[3] G. Benkart and E. Zelmanov, Lie algebras graded by finite root systems and intersection matrix algebras, Invent. Math. 126 (1996), no. 1, 1-45. [OpenAIRE]

[4] G. Benkart and O. Smirnov, Lie algebras graded by the root system BC1, J. Lie theory, 13 (2003), 91-132.

[5] S. Berman and R. Moody, Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy, Invent. Math. 108 (1992), no. 2, 323-347.

[6] V. Kac, Lie superalgebras, Adv. Math 26 (1977), 8-96.

[7] O. Loos, E. Neher, Locally finite root systems, Mem. Amer. Math. Soc. 171 (2004), no. 811, x+214.

[8] O. Loos, E. Neher, Reflection systems and partial root systems, Forum Math. 23 (2011), no. 2, 349-411.

[9] J. Morita and Y. Yoshii, Locally extended affine Lie algebras, J. Algebra 301 (1) (2006) 59-81.

[10] K.H. Neeb and N. Stumme, The classification of locally finite split simple Lie algebras, J. Reine angew. Math. 533 (2001), 25-53. [OpenAIRE]

[11] E. Neher, Extended affine Lie algebras and other generalization of affine Lie algebrasa survey, Developments and trends in infinite-dimensional Lie theory, 53-126, Prog. Math., 228, Birkhauser Boston, Inc., Boston, MA, 2011.

[12] E. Neher, Lie algebras graded by 3-graded root systems and Jordan pairs covered by grids, Amer. J. Math. 118 (1996), 439-491.

[13] I. Penkov, Classically Semisimple Locally Finite Lie Superalgebras, Forum Math. 16 (2004), no. 3, 431-446.

[14] G.B. Seligman, Rational methods in Lie algebras, M. Dekker Lect. Notes in pure and appl. math. 17, New York, 1976.

[15] V. Serganova, On generalizations of root systems, com. in algebra, 24(13) (1996), 4281-4299. [OpenAIRE]

17 references, page 1 of 2
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publication . Preprint . Article . 2013

Locally Finite Root Supersystems

Malihe Yousofzadeh;