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Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras

Drensky, Vesselin (2004)

Serdica Mathematical Journal

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.

On semi-invariants of tilted algebras of type Aₙ

Witold Kraśkiewicz (2001)

Colloquium Mathematicae

We prove that for algebras obtained by tilts from the path algebras of equioriented Dynkin diagrams of type Aₙ, the rings of semi-invariants are polynomial.

Polynomial identities of nil algebras of bounded index

Francesca Benanti, Vesselin Drensky (1999)

Bollettino dell'Unione Matematica Italiana

Lo scopo di questo lavoro è di dare una nuova descrizione del T -ideale generato dalla nil-identità x n = 0 come immagine omeomorfa della n -esima potenza tensoriale simmetrica dell'algebra associativa libera K ⁢ X su un campo K di caratteristica 0 . Come applicazione calcoliamo il carattere delle conseguenze multilineari di grado ≤ n + 2 dell'identità x n = 0 .

Pseudospectra and matrix behaviour

Thomas Ransford (2010)

Banach Center Publications

We study the extent to which the pseudospectra of a matrix determine other aspects of its behaviour, such as the growth of its powers and its unitary equivalence class.

Weak polynomial identities and their applications

Vesselin Drensky (2021)

Communications in Mathematics

Let R be an associative algebra over a field K generated by a vector subspace V . The polynomial f ( x 1 , ... , x n ) of the free associative algebra K 〈 x 1 , x 2 , ... 〉 is a weak polynomial identity for the pair ( R , V ) if it vanishes in R when evaluated on V . 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....

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