Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Almost monomial subalgebras of and their LAGBI bases

Kennerland, Erik ; Torstensson, Anna LU and Ufnarovski, Victor LU (2026) In Applicable Algebra in Engineering, Communications and Computing
Abstract

We investigate subalgebras of finite codimension in. In earlier work we have introduced a way of describing such subalgebras in terms of their so called (subalgebra) spectrum and a set of conditions for subalgebra membership that can be expressed by evaluating polynomials and their derivatives in points of the spectrum only. In this paper we focus on subalgebras with a single element in their spectrum. This includes, among others, all monomial subalgebras. Moreover, any subalgebra given by only conditions involving derivatives can be obtained as a finite intersection of algebras with single spectrum. Our main result is an efficient algorithm for finding the set of defining conditions given a set of generators for a single spectrum... (More)

We investigate subalgebras of finite codimension in. In earlier work we have introduced a way of describing such subalgebras in terms of their so called (subalgebra) spectrum and a set of conditions for subalgebra membership that can be expressed by evaluating polynomials and their derivatives in points of the spectrum only. In this paper we focus on subalgebras with a single element in their spectrum. This includes, among others, all monomial subalgebras. Moreover, any subalgebra given by only conditions involving derivatives can be obtained as a finite intersection of algebras with single spectrum. Our main result is an efficient algorithm for finding the set of defining conditions given a set of generators for a single spectrum subalgebra. As an important step on the way to an algorithm we introduce a new canonical basis (with many similarities to SAGBI basis), that we name LAGBI basis, for our single spectrum algebras. We then find an efficient algorithm for computing a LAGBI basis and finally incorporate it into our main algorithm for finding defining conditions. In the process we also find the derivations of a single spectrum subalgebra.

(Less)
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
in press
subject
keywords
Derivations, Polynomial subalgebra, SAGBI, Subalgebra spectrum
in
Applicable Algebra in Engineering, Communications and Computing
publisher
Springer
external identifiers
  • scopus:105027180273
ISSN
0938-1279
DOI
10.1007/s00200-025-00712-7
language
English
LU publication?
yes
id
ddf708c9-eebf-4674-b3fb-0f21760e1627
date added to LUP
2026-03-17 14:02:20
date last changed
2026-03-17 14:03:22
@article{ddf708c9-eebf-4674-b3fb-0f21760e1627,
  abstract     = {{<p>We investigate subalgebras of finite codimension in. In earlier work we have introduced a way of describing such subalgebras in terms of their so called (subalgebra) spectrum and a set of conditions for subalgebra membership that can be expressed by evaluating polynomials and their derivatives in points of the spectrum only. In this paper we focus on subalgebras with a single element in their spectrum. This includes, among others, all monomial subalgebras. Moreover, any subalgebra given by only conditions involving derivatives can be obtained as a finite intersection of algebras with single spectrum. Our main result is an efficient algorithm for finding the set of defining conditions given a set of generators for a single spectrum subalgebra. As an important step on the way to an algorithm we introduce a new canonical basis (with many similarities to SAGBI basis), that we name LAGBI basis, for our single spectrum algebras. We then find an efficient algorithm for computing a LAGBI basis and finally incorporate it into our main algorithm for finding defining conditions. In the process we also find the derivations of a single spectrum subalgebra.</p>}},
  author       = {{Kennerland, Erik and Torstensson, Anna and Ufnarovski, Victor}},
  issn         = {{0938-1279}},
  keywords     = {{Derivations; Polynomial subalgebra; SAGBI; Subalgebra spectrum}},
  language     = {{eng}},
  publisher    = {{Springer}},
  series       = {{Applicable Algebra in Engineering, Communications and Computing}},
  title        = {{Almost monomial subalgebras of and their LAGBI bases}},
  url          = {{http://dx.doi.org/10.1007/s00200-025-00712-7}},
  doi          = {{10.1007/s00200-025-00712-7}},
  year         = {{2026}},
}