Classification of exceptional train algebras of rank 3 and type (4, 2): step 1
Küçük Resim Yok
Tarih
2009
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Yayıncı
Maltepe Üniversitesi
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CC0 1.0 Universal
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
Özet
Let F be a field with char(F ) 6= 2, A a commutative F -algebra, not necessarily associative and ? : A ? F a nonzero homomorphism. If there exists ? ? F such that, for all x in A, x 3 ? (1 + ?)?(x)x 2 + ??(x) 2x = 0, then the pair (A, ?) is called a (commutative) train algebra of rank 3. When we consider 2? 6= 1, there is an idempotent e ? A and relative to this element, A has a Peirce decomposition A = F e ? Ue ? Ve, where Ue = {u ? Ker(w)N : 2eu = u} and Ve = {v ? Ker(w) : ev = ?v}. The type of A is the ordered pair of integers (1 + r, s), where r = dim(Ue) and s = dim(Ve). If A = F e ? Ue ? Ve is a train algebra of rank 3 and dimension 6, the possible types of A are (5, 1), (4, 2), (3, 3), (2, 4) and (1, 5). The train algebras of rank 3 and types (n, 1), (3, n - 2), (2, n - 1) and (1, n) had already been classified and so, in order to complete the classification of the train algebras of rank 3 and dimension 6, we have to analyse such algebras of type (4, 2). Here we begin this classification
Açıklama
Anahtar Kelimeler
Kaynak
International Conference of Mathematical Sciences
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Sayı
Künye
Arbach, R. ve Fernandes de Oliveira, L. A. (2009). Classification of exceptional train algebras of rank 3 and type (4, 2): step 1. s. 341.
