Asymptotics for Amitsur's Capelli-type polynomials and verbally prime PI-algebras

Benanti, Francesca; Sviridova, Irina

doi:10.1007/bf02773825

Cited by 6 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [3] this result was extended to finite dimensional simple superalgebras and in [6] the authors found similar result in the case of algebras with involution (for a survey see [7]). The link between the asymptotic of the codimensions of the Amitsur's Capelli-type polynomials and the verbally prime algebras was studied in [5].…”

Section: Introductionmentioning

confidence: 99%

*-Graded Capelli polynomials and their asymptotics

Benanti

Valenti

2022

Int. J. Algebra Comput.

View full text Add to dashboard Cite

Let [Formula: see text] be the free ∗-superalgebra over a field [Formula: see text] of characteristic zero and let [Formula: see text] be the [Formula: see text]-ideal generated by the set of the ∗-graded Capelli polynomials [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] alternating on [Formula: see text] symmetric variables of homogeneous degree zero, on [Formula: see text] skew variables of homogeneous degree zero, on [Formula: see text] symmetric variables of homogeneous degree one and on [Formula: see text] skew variables of homogeneous degree one, respectively. We study the asymptotic behavior of the sequence of ∗-graded codimensions of [Formula: see text] In particular, we prove that the ∗-graded codimensions of the finite dimensional simple ∗-superalgebras are asymptotically equal to the ∗-graded codimensions of [Formula: see text], for some fixed natural numbers [Formula: see text] and [Formula: see text].

show abstract

Section: Introductionmentioning

confidence: 99%

*-Graded Capelli polynomials and their asymptotics

Benanti

Valenti

2022

Int. J. Algebra Comput.

View full text Add to dashboard Cite

show abstract

“…., which is an important numerical characteristic of polynomial identities of A. Study of asymptotic behavior of {c n (A)} for associative algebras was started in the beginning of 70's (see, for example, [23], [15], [16]) and was continued during the subsequent decades (see, for example, [14], [6], [10], [3], [4], [5], [24] and also the bibliography in [11]). Later, similar numerical characteristics were considered for Lie algebras [17], [25], [18] and other non-associative algebras: Lie superalgebras [28] and their generalizations [22], Leibniz algebras [21], Jordan and alternative algebras [12], [9], Poisson and Novikov algebras [20], [8], etc.…”

Section: Introductionmentioning

confidence: 99%

On existence of PI-exponents of codimension growth

Zaicev¹

2014

ERA-MS

View full text Add to dashboard Cite

show abstract

“…In [4] these result was extended to finite dimensional simple superalgebras proving that the graded codimensions of the T 2 -ideal generated by the graded Capelli polynomials Γ M+1,L+1 , for some fixed M , L, are asymptotically equal to the graded codimensions of a simple finite dimensional superalgebra. The link between the asymptotic of the codimensions of the Amitsur's Capelli-type polynomials and the verbally prime algebras was studied in [5].…”

Section: Introductionmentioning

confidence: 99%

Asymptotics for Graded Capelli Polynomials

Benanti

2014

Algebr Represent Theor

Self Cite

View full text Add to dashboard Cite

The finite dimensional simple superalgebras play an important role in the theory\ud of PI-algebras in characteristic zero. The main goal of this paper is to characterize the T2-\ud ideal of graded identities of any such algebra by considering the growth of the corresponding\ud supervariety. We consider the T2-ideal M+1,L+1 generated by the graded Capelli polynomials\ud CapM+1[Y,X] and CapL+1[Z,X] alternanting on M + 1 even variables and L + 1\ud odd variables, respectively.We prove that the graded codimensions of a simple finite dimensional\ud superalgebra are asymptotically equal to the graded codimensions of the T2-ideal\ud M+1,L+1, for some fixed natural numbers M and L. In particular\ud c\ud sup\ud n ( k2+l2+1,2kl+1) c\ud sup\ud n (Mk,l(F ))\ud and\ud c\ud sup\ud n ( s2+1,s2+1) c\ud sup\ud n (Ms(F ⊕ tF)).\ud These results extend to finite dimensional superalgebras a theorem of Giambruno and\ud Zaicev [6] giving in the ordinary case the asymptotic equality\ud c\ud sup\ud n ( k2+1,1) c\ud sup\ud n (Mk(F ))\ud between the codimensions of the Capelli polynomials and the codimensions of the matrix\ud algebra Mk(F )

show abstract

Asymptotics for Amitsur's Capelli-type polynomials and verbally prime PI-algebras

Abstract: We consider associative P I-algebras over a field of characteristic zero. The main goal of the paper is to prove that the codimensions of a verbally prime algebra [11] are asymptotically equal to the codimensions of the T -ideal generated by some Amitsur's Capelli-type polynomials E *

Cited by 6 publications

References 16 publications

*-Graded Capelli polynomials and their asymptotics

*-Graded Capelli polynomials and their asymptotics

On existence of PI-exponents of codimension growth

Asymptotics for Graded Capelli Polynomials

Contact Info

Product

Resources

About