scholarly journals Graded Lie algebras of maximal class of type n

2021 ◽  
Author(s):  
Sandro Mattarei ◽  
Simone Ugolini
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Graded Lie Algebras

scholarly journals Graded Lie Algebras of Maximal Class

1997 ◽  
Vol 349 (10) ◽  
pp. 4021-4051 ◽  
Author(s):  
A. Caranti ◽  
S. Mattarei ◽  
M. F. Newman
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Graded Lie Algebras

scholarly journals Graded Lie algebras of maximal class, III

2005 ◽  
Vol 284 (2) ◽  
pp. 435-461 ◽  
Author(s):  
G. Jurman
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Class Iii ◽  
Graded Lie Algebras

scholarly journals Graded Lie Algebras of Maximal Class, II

2000 ◽  
Vol 229 (2) ◽  
pp. 750-784 ◽  
Author(s):  
A Caranti ◽  
M.F Newman
Keyword(s):  
Lie Algebras ◽  
Class Ii ◽  
Maximal Class ◽  
Graded Lie Algebras

scholarly journals Graded Lie algebras of maximal class of type p

2021 ◽  
Vol 588 ◽  
pp. 77-117 ◽  
Author(s):  
Valentina Iusa ◽  
Sandro Mattarei ◽  
Claudio Scarbolo
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Graded Lie Algebras

scholarly journals Cohomology of graded Lie algebras of maximal class

2006 ◽  
Vol 296 (1) ◽  
pp. 157-176 ◽  
Author(s):  
Alice Fialowski ◽  
Dmitri Millionschikov
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Graded Lie Algebras

scholarly journals On Varieties of Lie Algebras of Maximal Class

2015 ◽  
Vol 67 (1) ◽  
pp. 55-89 ◽  
Author(s):  
Tatyana Barron ◽  
Dmitry Kerner ◽  
Marina Tvalavadze
Keyword(s):  
Lie Algebras ◽  
Technical Condition ◽  
Partial Answer ◽  
Maximal Class ◽  
Graded Lie Algebras ◽  
Projective Varieties ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Filiform Lie Algebras ◽  
Complex Projective

AbstractWe study complex projective varieties that parametrize (finite-dimensional) filiform Lie algebras over ℂ, using equations derived by Millionshchikov. In the infinite-dimensional case we concentrate our attention on ℕ-graded Lie algebras of maximal class. As shown by A. Fialowski there are only three isomorphism types of ℕ-graded Lie algebras of maximal class generated by L1 and L2, L = 〈L1; L2〉. Vergne described the structure of these algebras with the property L = 〈L1〉. In this paper we study those generated by the first and q-th components where q > 2, L = 〈L1; Lq〉. Under some technical condition, there can only be one isomorphism type of such algebras. For q = 3 we fully classify them. This gives a partial answer to a question posed by Millionshchikov.

scholarly journals Some thin Lie algebras related to Albert-Frank algebras and algebras of maximal class

1999 ◽  
Vol 67 (2) ◽  
pp. 157-184 ◽  
Author(s):  
A. Caranti ◽  
S. Mattarei
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Loop Algebra ◽  
Maximal Class ◽  
Graded Lie Algebras ◽  
Simple Lie Algebras ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Wide Range ◽  
Graded Lie Algebra

AbstractWe investigate a class of infinite-dimensional, modular, graded Lie algebra in which the homogeneous components have dimension at most two. A subclass of these algebras can be obtained via a twisted loop algebra construction from certain finite-dimensional, simple Lie algebras of Albert-Frank type.Another subclass of these algebras is strictly related to certain graded Lie algebras of maximal class, and exhibits a wide range of behaviours.

THE STRUCTURE OF THIN LIE ALGEBRAS WITH CHARACTERISTIC TWO

2010 ◽  
Vol 20 (06) ◽  
pp. 731-768
Author(s):  
MARINA AVITABILE ◽  
GIUSEPPE JURMAN ◽  
SANDRO MATTAREI
Keyword(s):  
Lie Algebras ◽  
Positive Characteristic ◽  
Maximal Class ◽  
Initial Structure ◽  
Graded Lie Algebras ◽  
Characteristic P ◽  
Infinite Dimensional ◽  
Loop Algebras ◽  
Finite Dimensional ◽  
Characteristic Two

Thin Lie algebras are graded Lie algebras [Formula: see text] with dim Li ≤ 2 for all i, and satisfying a more stringent but natural narrowness condition modeled on an analogous condition for pro-p-groups. The two-dimensional homogeneous components of L, which include L1, are named diamonds. Infinite-dimensional thin Lie algebras with various diamond patterns have been produced, over fields of positive characteristic, as loop algebras of suitable finite-dimensional simple Lie algebras, of classical or of Cartan type depending on the location of the second diamond. The goal of this paper is a description of the initial structure of a thin Lie algebra, up to the second diamond. Specifically, if Lk is the second diamond of L, then the quotient L/Lk is a graded Lie algebras of maximal class. In odd characteristic p, the quotient L/Lk is known to be metabelian, and hence uniquely determined up to isomorphism by its dimension k, which ranges in an explicitly known set of possible values: 3, 5, a power of p, or one less than twice a power of p. However, the quotient L/Lk need not be metabelian in characteristic two. We describe here all the possibilities for L/Lk up to isomorphism. In particular, we prove that k + 1 equals a power of two.

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