SYMPLECTIC ALTERNATING ALGEBRAS
نویسندگان
چکیده
منابع مشابه
Symplectic alternating nil-algebras
In this paper we continue developing the theory of symplectic alternating algebras that was started in [3]. We focus on nilpotency, solubility and nil-algebras. We show in particular that symplectic alternating nil-2 algebras are always nilpotent and classify all nil-algebras of dimension up to 8.
متن کاملSymplectic Alternating Algebras
This paper begins the development of a theory of what we will call symplectic alternating algebras. They have arisen in the study of 2-Engel groups but seem also to be of interest in their own right. The main part of the paper deals with the challenging classification of some algebras of this kind which arise in the context of 2-Engel groups and give some new information about these groups. The...
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A symplectic alternating algebra (SAA) is a symplectic vector space L, whose associated alternating form is non-degenerate, that is furthermore equipped with a binary alternating product · : L× L 7→ L with the extra requirement that (x · y, z) = (y · z, x) for all x, y, z ∈ L. This condition can be expressed equivalently by saying that (u · x, v) = (u, v · x) for all u, v, x ∈ L or in other wor...
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We develop a structure theory for nilpotent symplectic alternating algebras.
متن کاملNilpotent symplectic alternating algebras II
In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class C of 2-Engel 3-groups of exponent 27 and under this correspondance we will see that the nilpotent algebras corre...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2008
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196708004585