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- Cantuba, Rafael RenoDe La Salle University, Malate, Manila, Philippines (author)
Lie polynomial characterization problems
- Article/chapterEnglish2020
Publisher, publication year, extent ...
- 2020-06-19
- Cham :Springer Nature,2020
- printrdacarrier
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- LIBRIS-ID:oai:DiVA.org:mdh-49446
- https://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49446URI
- https://doi.org/10.1007/978-3-030-41850-2_25DOI
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- Language:English
- Summary in:English
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- We present a review of some results about Lie polynomials in finitely-generated associative algebras with defining relations that involve deformed commutation relations. Such algebras have arisen from various areas such as in the theory of quantum groups, of q-oscillators, of q-deformed Heisenberg algebras, of orthogonal polynomials, and even from algebraic combinatorics. The q-deformed Heisenberg-Weyl relation is so far the most successful setting for a Lie polynomial characterization problem. Both algebraic and operator-theoretic approaches have been found. We also discuss some partial results for other algebras related to quantum groups.
Subject headings and genre
- NATURVETENSKAP Matematik Algebra och logik hsv//swe
- NATURAL SCIENCES Mathematics Algebra and Logic hsv//eng
- Lie polynomial
- Lie subalgebra
- generators and relations
- diamond lemma
- associative algebra
- Mathematics/Applied Mathematics
- matematik/tillämpad matematik
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- Silvestrov, Sergei,Professor,1970-Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM(Swepub:mdh)ssv01 (author)
- De La Salle University, Malate, Manila, PhilippinesUtbildningsvetenskap och Matematik (creator_code:org_t)
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- In:Algebraic Structures and ApplicationsCham : Springer Nature, s. 593-6019783030418496
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