An Extended Freudenthal Magic Square in characteristic 3

Cunha, Isabel; Elduque, Alberto

doi:10.1016/j.jalgebra.2007.07.028

Cited by 23 publications

(52 citation statements)

References 17 publications

(36 reference statements)

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“…Elduque [17,18,13,14] considered a particular case of the problem (9.1) and arranged the Lie (super)algebras he discovered in a Supermagic Square all its entries being of the form g(A). These Elduque and Cunha superalgebras are, indeed, exceptional ones.…”

Section: )mentioning

confidence: 99%

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Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix

Bouarroudj

Grozman

Leites

2009

SIGMA

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Abstract. Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the corresponding Lie superalgebra is simple otherwise the quotient of the derived Lie superalgebra modulo center is simple (if its rank is greater than 1). Eleven new exceptional simple modular Lie superalgebras are discovered. Several features of classic notions, or notions themselves, are clarified or introduced, e.g., Cartan matrix, several versions of restrictedness in characteristic 2, Dynkin diagram, Chevalley generators, and even the notion of Lie superalgebra if the characteristic is equal to 2. Interesting phenomena in characteristic 2: (1) all simple Lie superalgebras with Cartan matrix are obtained from simple Lie algebras with Cartan matrix by declaring several (any) of its Chevalley generators odd; (2) there exist simple Lie superalgebras whose even parts are solvable. The Lie superalgebras of fixed points of automorphisms corresponding to the symmetries of Dynkin diagrams are also listed and their simple subquotients described.

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Section: )mentioning

confidence: 99%

“…Observe that although several of the exceptional examples were known for p > 2, together with one indecomposable Cartan matrix per each Lie superalgebra [17,18,13,14], the complete description of all inequivalent Cartan matrices for all the exceptional Lie superalgebras of the form g(A) and for ALL cases for p = 2 is new.…”

mentioning

confidence: 99%

Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix

Bouarroudj

Grozman

Leites

2009

SIGMA

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“…Заметим, что это определение эквивалентно данному в [22] определению контрагре-диентной алгебры Ли, хотя записано слегка иначе. Условие (17), будучи модифи-цировано в максимальный однородный идеал s такой, что s ∩ h = c,…”

Section: теорема 4 алгебра ли O(5)unclassified

Деформации алгебры Ли $\mathfrak o(5)$ в характеристиках $3$ и $2$

Буаррудж¹,

Bouarroudj²,

Lebedev³

et al. 2011

Mat. Zametki

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“…Also, denote by S 1,2 the para-Hurwitz superalgebra B(1, 2), and by S 4,2 the para-Hurwitz superalgebra B(4, 2). Then the Lie superalgebras g(S, S ), where S, S run over {S 1 , S 2 , S 4 , S 8 , S 1,2 , S 4,2 }, appear in Table 1, which has been obtained in [Cunha and Elduque 2007a].…”

Section: The Supermagic Square In Characteristicmentioning

confidence: 99%