Special finite-dimensional algebras Appendix A. PI algebras satisfying a Capelli identity 23.2. Codimension growth for algebras satisfying a Capelli identity 23.1. The codimension estimate for matrices Chapter 23. The exponent of an associative PI algebra 21.3. Grassmann envelope and finite-dimensional superalgebras Chapter 20. The representability theorem, Theorem 19.7.4 19.8. Finitely generated PI superalgebras 19.6. Complements of commutative algebra and invariant theory 18.3. Rationality and a canonical filtration 18.2. The abstract Cayley–Hamilton theorem Chapter 18. The representability theorem, Theorem 17.1.1 17.5. Finite-dimensional and affine PI algebras 17.1. The theorem of Bergman and Lewin Chapter 17. ?-ideals of identities of block-triangular matrices 16.4. The unramified locus and restriction maps Chapter 15. Semisimple representations of CH algebras 14.4. The universal embedding into matrices 14.3.

Symplectic and orthogonal case Chapter 14. The alternating central polynomials Chapter 13. Representations of algebras with trace 12.3. The structure of generic 2×2 matrices Part 3. Some applications of Shirshov’s height theorem 8.3. Application: A theorem of Kemer Chapter 8. Cocharacters are supported on a (?,ℓ) hook 7.6.

Combinatorial aspects of polynomial identities Chapter 7. Separable and Azumaya algebras Chapter 6. Azumaya algebras and irreducible representations 5.1. The Schur algebra of the free algebra Chapter 5. The universal map into matrices Chapter 4. Symmetric functions and matrix invariants 3.1. Matrices and the standard identity Chapter 3. Table of contents : Cover Title page Preface The plan of the book Differences with other books Introduction 0.1.

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