Free Lie Algebras, Generalized Witt Formula, and the Denominator Identity
Identifieur interne : 001A97 ( Main/Exploration ); précédent : 001A96; suivant : 001A98Free Lie Algebras, Generalized Witt Formula, and the Denominator Identity
Auteurs : Seok-Jin Kang [Corée du Sud] ; Myung-Hwan Kim [Corée du Sud]Source :
- Journal of Algebra [ 0021-8693 ] ; 1996.
English descriptors
- KwdEn :
- Algebra, Combinatorial, Combinatorial identities, Combinatorial identity, Countable abelian semigroup, Denominator, Denominator identity, Denominator identity yields, Dimension formula, Ector, Ector space, Elliptic, Form dimension formula, Formal power series, Generalized algebras, Gradation, Homogeneous subspaces, Homology, Homology modules, Js1v, Kang, Module, Mqnyc, Nsy1, Other hand, Positive integer, Positive integers, Product formula, Vector space, Witt, Witt formula, Witt partition function, Witt partition functions.
- Teeft :
- Algebra, Combinatorial, Combinatorial identities, Combinatorial identity, Countable abelian semigroup, Denominator, Denominator identity, Denominator identity yields, Dimension formula, Ector, Ector space, Elliptic, Form dimension formula, Formal power series, Generalized algebras, Gradation, Homogeneous subspaces, Homology, Homology modules, Js1v, Kang, Module, Mqnyc, Nsy1, Other hand, Positive integer, Positive integers, Product formula, Vector space, Witt, Witt formula, Witt partition function, Witt partition functions.
Abstract
Abstract: Let Γ be a countable abelian semigroup satisfying a suitable finiteness condition, and letL=⊕α∈ΓLαbe the free Lie algebra generated by a Γ-graded vector spaceVoverC. In this paper, from the denominator identity, we derive a dimension formula for the homogeneous subspaces of the free Lie algebraL=⊕α∈ΓLαand discuss numerous applications of our dimension formula to various interesting cases. Our dimension formula will be expressed in terms of the Witt partition functions. Various expressions of the Witt partition functions will give rise to a number of interesting combinatorial identities. As a special case, we obtain a recursive relation for the coefficients of the elliptic modular functionj.
Url:
DOI: 10.1006/jabr.1996.0233
Affiliations:
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formula</term><term>Witt partition function</term><term>Witt partition functions</term></keywords><keywords scheme="Teeft" xml:lang="en"><term>Algebra</term><term>Combinatorial</term><term>Combinatorial identities</term><term>Combinatorial identity</term><term>Countable abelian semigroup</term><term>Denominator</term><term>Denominator identity</term><term>Denominator identity yields</term><term>Dimension formula</term><term>Ector</term><term>Ector space</term><term>Elliptic</term><term>Form dimension formula</term><term>Formal power series</term><term>Generalized algebras</term><term>Gradation</term><term>Homogeneous subspaces</term><term>Homology</term><term>Homology modules</term><term>Js1v</term><term>Kang</term><term>Module</term><term>Mqnyc</term><term>Nsy1</term><term>Other hand</term><term>Positive integer</term><term>Positive integers</term><term>Product formula</term><term>Vector space</term><term>Witt</term><term>Witt formula</term><term>Witt partition function</term><term>Witt partition functions</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Let Γ be a countable abelian semigroup satisfying a suitable finiteness condition, and letL=⊕α∈ΓLαbe the free Lie algebra generated by a Γ-graded vector spaceVoverC. In this paper, from the denominator identity, we derive a dimension formula for the homogeneous subspaces of the free Lie algebraL=⊕α∈ΓLαand discuss numerous applications of our dimension formula to various interesting cases. Our dimension formula will be expressed in terms of the Witt partition functions. Various expressions of the Witt partition functions will give rise to a number of interesting combinatorial identities. As a special case, we obtain a recursive relation for the coefficients of the elliptic modular functionj.</div></front></TEI><affiliations><list><country><li>Corée du Sud</li></country><settlement><li>Séoul</li></settlement><orgName><li>Université nationale de Séoul</li></orgName></list><tree><country name="Corée du Sud"><noRegion><name sortKey="Kang, Seok Jin" sort="Kang, Seok Jin" uniqKey="Kang S" first="Seok-Jin" last="Kang">Seok-Jin Kang</name></noRegion><name sortKey="Kim, Myung Hwan" sort="Kim, Myung Hwan" uniqKey="Kim M" first="Myung-Hwan" last="Kim">Myung-Hwan Kim</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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