Hilbert series of T-spaces

A. Ya Belov; L. Centrone; S. Malev

doi:10.1016/j.jalgebra.2023.03.018

Hilbert series of T-spaces

A. Ya Belov, L. Centrone, S. Malev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the Hilbert series of a T-space in a free associative algebra A is either a rational function, or differs from the Hilbert series of the commutator [A,A] by a rational function.

Original language	English
Pages (from-to)	350-361
Number of pages	12
Journal	Journal of Algebra
Volume	628
DOIs	https://doi.org/10.1016/j.jalgebra.2023.03.018
State	Published - 15 Aug 2023

Bibliographical note

Funding Information:
This work was supported by Israel Science Foundation , grant No 1994/20 .

Funding Information:
We are grateful to Professor A.V. Mikhalev, who past away 27-th of October of 2022, for useful discussions and to the referee for his/her remarks and suggestions. This work was supported by Israel Science Foundation, grant No 1994/20. The authors are also deeply grateful to the referee: her/his suggestions improved significantly the exposition of the paper. The second author wants to thank GNSAGA of Istituto Nazionale di Alta Matematica (INDAM).

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

Hilbert series
PI-algebra
Regular word
T-space

Access to Document

10.1016/j.jalgebra.2023.03.018

Cite this

@article{289e7b7ed0b044cd8c22959f1e5b72c7,

title = "Hilbert series of T-spaces",

abstract = "We show that the Hilbert series of a T-space in a free associative algebra A is either a rational function, or differs from the Hilbert series of the commutator [A,A] by a rational function.",

keywords = "Hilbert series, PI-algebra, Regular word, T-space",

author = "Belov, {A. Ya} and L. Centrone and S. Malev",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

month = aug,

day = "15",

doi = "10.1016/j.jalgebra.2023.03.018",

language = "אנגלית",

volume = "628",

pages = "350--361",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Hilbert series of T-spaces

AU - Belov, A. Ya

AU - Centrone, L.

AU - Malev, S.

PY - 2023/8/15

Y1 - 2023/8/15

N2 - We show that the Hilbert series of a T-space in a free associative algebra A is either a rational function, or differs from the Hilbert series of the commutator [A,A] by a rational function.

AB - We show that the Hilbert series of a T-space in a free associative algebra A is either a rational function, or differs from the Hilbert series of the commutator [A,A] by a rational function.

KW - Hilbert series

KW - PI-algebra

KW - Regular word

KW - T-space

UR - http://www.scopus.com/inward/record.url?scp=85151686040&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2023.03.018

DO - 10.1016/j.jalgebra.2023.03.018

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85151686040

SN - 0021-8693

VL - 628

SP - 350

EP - 361

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Hilbert series of T-spaces

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this