2000 Mathematics Subject Classification: 16R10, 16R30. The classical theorem of Weitzenböck states that the algebra of invariants K[X]^g of a single unipotent transformation g ∈ GLm(K) acting on the polynomial algebra K[X] = K[x1, . . . , xm] over a field K of characteristic 0 is finitely generated. Partially supported by Grant MM-1106/2001 of the Bulgarian National Science Fund.
Let be an associative algebra over a field generated by a vector subspace . The polynomial of the free associative algebra is a weak polynomial identity for the pair if it vanishes in when evaluated on . We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three....
2010 Mathematics Subject Classification: 05A15, 05E05, 05E10, 13A50, 15A72, 16R10, 16R30, 20G05 Let K be a field of any characteristic. Let the formal power series f(x1, ..., xd) = ∑ αnx1^n1 ··· xd^nd = ∑ m(λ)Sλ(x1, ..., xd), αn, m(λ) ∈ K, be a symmetric function decomposed as a series of Schur functions. When f is a rational function whose denominator is a product of binomials of the form 1−x1^a1 ··· xd^ad, we use a classical combinatorial method of Elliott of 1903 further developed...
Lo scopo di questo lavoro è di dare una nuova descrizione del -ideale generato dalla nil-identità come immagine omeomorfa della -esima potenza tensoriale simmetrica dell'algebra associativa libera su un campo di caratteristica . Come applicazione calcoliamo il carattere delle conseguenze multilineari di grado dell'identità .
Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra over a field of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordinates of . In particular, the two nontrivial coordinates in the Anick automorphism are both wild. We establish a...
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