Structure of free semigroupoid algebras.
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| Title: | Structure of free semigroupoid algebras. |
|---|---|
| Authors: | Davidson, Kenneth R.1 (AUTHOR) krdavids@uwaterloo.ca, Dor-On, Adam1,2 (AUTHOR) adoron@illinois.edu, Li, Boyu1,3 (AUTHOR) boyuli@uvic.ca |
| Source: | Journal of Functional Analysis. Nov2019, Vol. 277 Issue 9, p3283-3350. 68p. |
| Subjects: | Semigroup algebras, Algebra, Structural analysis (Engineering), Mathematical equivalence, Reflexivity |
| Abstract: | A free semigroupoid algebra is the wot -closure of the algebra generated by a TCK family of a graph. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role of absolute continuity and wandering vectors. These results are applied to obtain a Lebesgue-von Neumann-Wold decomposition of TCK families, along with reflexivity, a Kaplansky density theorem and classification for free semigroupoid algebras. Several classes of examples are discussed and developed, including self-adjoint examples and a classification of atomic free semigroupoid algebras up to unitary equivalence. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 138293794 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Structure of free semigroupoid algebras. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Davidson%2C+Kenneth+R%2E%22">Davidson, Kenneth R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> krdavids@uwaterloo.ca</i><br /><searchLink fieldCode="AR" term="%22Dor-On%2C+Adam%22">Dor-On, Adam</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> adoron@illinois.edu</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Boyu%22">Li, Boyu</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> boyuli@uvic.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Nov2019, Vol. 277 Issue 9, p3283-3350. 68p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Semigroup+algebras%22">Semigroup algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+analysis+%28Engineering%29%22">Structural analysis (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+equivalence%22">Mathematical equivalence</searchLink><br /><searchLink fieldCode="DE" term="%22Reflexivity%22">Reflexivity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A free semigroupoid algebra is the wot -closure of the algebra generated by a TCK family of a graph. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role of absolute continuity and wandering vectors. These results are applied to obtain a Lebesgue-von Neumann-Wold decomposition of TCK families, along with reflexivity, a Kaplansky density theorem and classification for free semigroupoid algebras. Several classes of examples are discussed and developed, including self-adjoint examples and a classification of atomic free semigroupoid algebras up to unitary equivalence. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jfa.2019.06.002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 68 StartPage: 3283 Subjects: – SubjectFull: Semigroup algebras Type: general – SubjectFull: Algebra Type: general – SubjectFull: Structural analysis (Engineering) Type: general – SubjectFull: Mathematical equivalence Type: general – SubjectFull: Reflexivity Type: general Titles: – TitleFull: Structure of free semigroupoid algebras. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Davidson, Kenneth R. – PersonEntity: Name: NameFull: Dor-On, Adam – PersonEntity: Name: NameFull: Li, Boyu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 00221236 Numbering: – Type: volume Value: 277 – Type: issue Value: 9 Titles: – TitleFull: Journal of Functional Analysis Type: main |
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