Lie isomorphisms of triangular and block-triangular matrix algebras over commutative rings

Simple item page
dc.contributor.authorCecil, Anthony John
dc.contributor.supervisorSourour, A. R.
dc.date.accessioned2016-08-24T15:12:16Z
dc.date.available2016-08-24T15:12:16Z
dc.date.copyright2016en_US
dc.date.issued2016-08-24
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractFor many matrix algebras, every associative automorphism is inner. We discuss results by Đoković that a non-associative Lie automorphism φ of a triangular matrix algebra Tₙ over a connected unital commutative ring, is of the form φ(A)=SAS⁻¹ + τ(A)I or φ(A)=−SJ Aᵀ JS⁻¹ + τ(A)I, where S ∈ Tₙ is invertible, J is an antidiagonal permutation matrix, and τ is a generalized trace. We incorporate additional arguments by Cao that extended Đoković’s result to unital commutative rings containing nontrivial idempotents. Following this we develop new results for Lie isomorphisms of block upper-triangular matrix algebras over unique factorization domains. We build on an approach used by Marcoux and Sourour to characterize Lie isomorphisms of nest algebras over separable Hilbert spaces. We find that these Lie isomorphisms generally follow the form φ = σ + τ where σ is either an associative isomorphism or the negative of an associative anti-isomorphism, and τ is an additive mapping into the center, which maps commutators to zero. This echoes established results by Martindale for simple and prime rings.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/7471
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/2.5/ca/*
dc.subjectMathematicsen_US
dc.subjectLinear Algebraen_US
dc.subjectMatrix Algebrasen_US
dc.subjectRing Theoryen_US
dc.subjectLie Isomorphismsen_US
dc.subjectTriangular Algebrasen_US
dc.subjectBlock-Triangular Algebrasen_US
dc.titleLie isomorphisms of triangular and block-triangular matrix algebras over commutative ringsen_US
dc.typeThesisen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Cecil_Anthony_MSc_2016.pdf
Size:
282.72 KB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.74 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Electronic Theses and Dissertations (ETD)
 
University of Victoria Libraries

We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.