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Rings with Polynomial Identities and Finite Dimensional Representations of Algebras
About this Title
Eli Aljadeff, Technion-Israel Institute of Technology, Haifa, Israel, Antonio Giambruno, Universitá di Palermo, Palermo, Italy, Claudio Procesi, Universitá di Roma "La Sapienza", Roma, Italy and Amitai Regev, The Weizmann Institute of Science, Rehovot, Israel
Publication: Colloquium Publications
Publication Year:
2020; Volume 66
ISBNs: 978-1-4704-5174-5 (print); 978-1-4704-5695-5 (online)
DOI: https://doi.org/10.1090/coll/066
Table of Contents
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Front/Back Matter
Chapters
Foundations
- Noncommutative algebra
- Universal algebra
- Symmetric functions and matrix invariants
- Polynomial maps
- Azumaya algebras and irreducible representations
- Tensor symmetry
Combinatorial aspects of polynomial identities
- Growth
- Shirshov’s theorem
- $2\times 2$ matrices
- The structure theorems
- Matrix identities
- Structure theorems
- Invariants and trace identities
- Involutions and matrices
- A geometric approach
- Spectrum and dimension
The relatively free algebras
- The nilpotent radical
- Finite-dimensional and affine PI algebras
- The relatively free algebras
- Identities and superalgebras
- The Specht problem
- The PI-exponent
- Codimension growth for matrices
- Codimension growth for algebras satisfying a Capelli identity
- The Golod–Shafarevich counterexamples
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