TY - JOUR
T1 - The Roots of Exceptional Modular Lie Superalgebras with Cartan Matrix
AU - Bouarroudj, Sofiane
AU - Leites, Dimitry
AU - Lozhechnyk, Olexander
AU - Shang, Jin
N1 - Publisher Copyright:
© 2020, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - For each of the exceptional (not entering infinite series) finite-dimensional modular Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots, and the corresponding Chevalley basis, for one of its inequivalent Cartan matrices, namely the one corresponding to the greatest number of mutually orthogonal isotropic odd simple roots (this number, called the defect of the Lie superalgebra, is important in the representation theory). Our main tools: Grozman’s Mathematica-based code SuperLie, Python, and A. Lebedev’s help.
AB - For each of the exceptional (not entering infinite series) finite-dimensional modular Lie superalgebras with indecomposable Cartan matrix, we give the explicit list of its roots, and the corresponding Chevalley basis, for one of its inequivalent Cartan matrices, namely the one corresponding to the greatest number of mutually orthogonal isotropic odd simple roots (this number, called the defect of the Lie superalgebra, is important in the representation theory). Our main tools: Grozman’s Mathematica-based code SuperLie, Python, and A. Lebedev’s help.
KW - Cartan matrix
KW - Modular Lie superalgebra
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U2 - 10.1007/s40598-020-00135-x
DO - 10.1007/s40598-020-00135-x
M3 - Article
AN - SCOPUS:85082870809
SN - 2199-6792
VL - 6
SP - 63
EP - 118
JO - Arnold Mathematical Journal
JF - Arnold Mathematical Journal
IS - 1
ER -