Keywords
- Conjugacy Class
- Closed Subset
- Algebraic Group
- Isomorphism Class
- Invariant Theory
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References
Borho, W., Kraft, H.: Ueber Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. Helv. 54 (1979), 61–104
Hesselink, W.: Singularities in the nilpotent scheme of a classical group. Trans. Amer. Math. Soc. 222 (1976), 1–32
Kraft, H.: Parametrisierung von Konjugationsklassen in sln. Math. Ann. 234 (1978), 209–220.
Kraft, H., Procesi, C.: Closures of Conjugacy Classes of Matrices are Normal. Invent. math. 53 (1979), 227–247
Peterson, D.: Geometry of the adjoint representation of a complex semisimple Lie algebra. Thesis Harvard University (1978)
Peterson, D.: Affine Cross-Sections for gl/GL. Harvard University, Cambridge, Mass.
Procesi, C., Kraft, H.: Classi coniugate in GL(n, ℂ). Rend. Sem. Mat. Univ. Padova 59 (1978), 209–222.
References
Gelfand; I.M. and Ponomarëv V.A.: Non decomposable representations of the Lorentz group, Usp. Mat. Nauk. 23 (1968), 3–60
Luna, D.: Slices étales. Bull. Soc. math. France, Mémoire 33 (1973), 81–105
Procesi, C.: Finite dimensional representations of algebras. Israel J. Math. 19(1974), 169–182
Procesi, C.: The invariant theory of n×n matrices. Adv. math. 19(1976), 306–381
Richardson, R.W.: Commuting varieties of semisimple Lie algebras and algebraic groups. compositio Math. 38 (1979), 311–327.
References
Hazewinkel, M.: A partial survey of the uses of algebraic geometry in system and control theory. Sym. Math. INDAM (Severi Centennial Conference, 1979), Academic Press
Tannenbaum, A.: Invariance and System Theory: Algebraic and Geometric Aspects. Lecture Notes in Math. 845 (1981), Springer-Verlag
References for chapter II
Birkes, D.: Orbits of linear algebraic groups. Ann Math. 93 (1971), 459–475
Borho, W., Kraft, H.: Ueber Bahnen und deren Deformationnen bei linearen Aktionen reduktiver Gruppen. Comment. Math. 54 (1979), 61–104
Fogarty, J.: Invariant Theory. W. A. Benjamin, Inc., New York, Amsterdam (1968)
Gabriel, P.: Finite representation type is open. In: Representations of Algebras. Proceedings of the International Conference, Ottawa 1974. Springer LN 488 (1975), 132–155
Hesselink, W.: Desingularizations of Varieties of Nullforms. Invent. Math. 55 (1979), 141–163
Kempf, G.: Instability in Invariant Theory. Ann. Math. 108 (1978), 299–316
Kraft, H.: Geometrische Methoden in der Invariantentheorie. Vieweg-Verlag (forthcoming)
Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoires 33 (1973), 81–105
Mazzola, G.: The algebraic and geometric classification of associative algebras of dimension five. Manuscripta Math. 27 (1979), 81–101
Mazzola, G.: Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. 55 (1980), 267–293
Mumford, D.: Geometric Invariant Theory. Erg. d. Math. 34 (1970). Springer-Verlag: Berlin-Heidelberg-New York
Procesi, C.: Finite dimensional representations of algebras. Israel J. Math. 19 (1974), 169–182
Springer, T. A.: Invariant Theory. Springer LN 585 (1977)
References for chapter III
Auslander, M.: Representation theory of artin algebras II. Comm. Algebra 1 (1974), 269–310
Gabriel, P.: Finite representation type is open. In: Representations of Algebras. Proceedings of the International Conference, Ottawa 1974. Springer LN 488 (1975), 132–155
Nazarova, L.A.; Roiter, A.V.: Categorical matricial problems and the conjecture of Brauer-Thrall (Russian) preprint, Inst. Math. Acad. Sci., Kiev 1973, German translation in Mitt. Math. Sem. Giessen 115 (1975)
References
Auslander, M.: Representation theory of artin algebras II. Comm. Algebra 1 (1974), 269–310
Birkes, D.: Orbits of linear algebraic groups. Ann. Math. 93 (1971), 459–475
Borho, W., Kraft, H.: Ueber Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. 54. (1979), 61–104
Fogarty, J.: Invariant Theory. W. A. Benjamin, Inc., New York, Amsterdam (1968)
Gabriel, P.: Finite representation type is open. In: Representations of Algebras. Proceedings of the International Conference, Ottawa 1974. Springer LN 488 (1975), 132–155
Gelfand, I. M. and Ponomarëv V. A.: Non decomposable representations of the Lorentz group, Usp. Mat. Nauk. 23 (1968), 3–60
Hazewinkel, M.: A partial survey of the uses of algebraic geometry in system and control theory. Sym. Math. INDAM (Severi Centennial Conference, 1979), Academic Press
Hesselink, W.: singularities in the nilpotent scheme of a classical group. Trans. Amer. Math. Soc. 222 (1976), 1–32
Hesselink, W.: Desingularizations of Varieties of Nullforms. Invent. Math. 55 (1979), 141–163
Kempf, G. Instability in Invariant Theory. Ann. Math. 108 (1978). 299–316
Kraft, H.: Parametrisierung von Konjugationsklassen in sln. Math. Ann. 234 (1978), 209–220
Kraft, H.: Geometrische Methoden in der Invariantentheorie. Vieweg-Verlag (forthcoming)
Kraft, H., Procesi, C.: Closures of Conjugacy Classes of Matrices are Normal. Invent. math. 53 (1979), 227–247
Luna, D.: Slices étales. Bull. Soc. Math. France, Mémoires 33 (1973), 81–105
Mazzola, G.: The algebraic and geometric classification of associative algebras of dimension five. Manuscripta Math. 27 (1979), 81–101
Mazzola, G.: Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. 55 (1980), 267–293
Mumford, D.: Geometric Invariant Theory. Erg. d. Math. 34 (1970). Springer-Verlag: Berlin-Heidelberg-New York
Nazarova, L. A., Roiter, A. V.: Catgorical matricial problems and the conjecture of Brauer-Thrall (Russian) preprint, Inst. Math. Acad. Sci., Kiev 1973, German translation in Mitt. Math. Sem. Giessen 115 (1975)
Peterson, D.: Geometry of the adjoint representation of a complex semisimple Lie algebra. Thesis Harvard University (1978)
Peterson, D.: Affine Cross-Sections for gl/GL. Harvard University, Cambridge, Mass.
Procesi, C.: Finite dimensional representations of algebras. Israel J. Math. 19 (1974), 169–182
Procesi, C.: The Invariant Theory of nxn matrices. 19 (1976), 306–381
Procesi C., Kraft, H.: Classi coniugate in GL (n, ℂ). Rend. Sem. Mat. Univ. Padova 59 (1978), 209–222
Richardson, R. W.: Commuting varieties of semisimple Lie algebras and algebraic groups. Composition Math. 38 (1979), 311–327
Springer, T. A.: Invariant Theory. Springer LN 585 (1977)
Tannenbaum, A.: Invariance and System Theory: Algebraic and Geometric Aspects. Lecture Notes in Math. 845 (1981), Springer-Verlag
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Kraft, H. (1982). Geometric methods in representation theory. In: Auslander, M., Lluis, E. (eds) Representations of Algebras. Lecture Notes in Mathematics, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094059
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DOI: https://doi.org/10.1007/BFb0094059
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