Abstract
This is the first part of our study of the existence ofAuslander–Reiten sequences of group representations. In this part weconsider representations of group schemes in characteristic 0; in Part II weconsider representations of group schemes in characteristic p; andin Part III we give applications to representations of groups and Liealgebras.
Similar content being viewed by others
References
Auslander, M., Reiten, I. and Smalø S. O.: Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, Cambridge, 1995.
Benson, D.: Representations and Cohomology I: Basic Representation Theory of Finite Groups and Associative Algebras, Cambridge Stud. Adv. Math. 30, Cambridge Univ. Press, Cambridge, 1991.
Benson, D. and Carlson, J. F.: Nilpotent elements in the Green ring, J. Algebra 104(1986), 329–350.
Borel, A.: Linear Algebraic Groups, 2nd edn, Grad. Texts in Math. 126, Springer, New York, 1991.
Demazure, M. and Grothendieck, A. (dirig.): Schemas en groupes I, Séminaire de géometrie algébrique du Bois Marie 1962/64 SGA 3, Lecture Notes in Math. 151, Springer, Berlin, 1970.
Donkin, S.: On projective modules for algebraic groups, J. London Math. Soc. 54(1996), 75–88.
Fröhlich, A.: Formal Groups, Lecture Notes in Math. 74, Springer, Berlin, 1968.
Green, J. A.: Locally finite representations, J. Algebra 41(1976), 131–171.
Hochschild, G. P.: Basic Theory of Algebraic Groups and Lie Algebras, Grad. Texts in Math. 75, Springer, Berlin, 1981.
Jantzen, J. C.: Representations of Algebraic Groups, Pure Appl. Math. 131, Academic Press, New York, 1987.
Lazard, M.: Sur les groupes de Lie formels à une paramètre, Bull. Soc. Math. France 83(1955), 251–274.
Oberst, U.: Affine Quotientenschemata nach affinen algebraischen Gruppen und induzierte Darstellungen, J. Algebra 44(1977), 503–538.
Takeuchi, M.: A correspondence between Hopf ideals and sub-Hopf algebras, Manuscripta Math. 7(1972), 251–270.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Donkin, S. On the Existence of Auslander–Reiten Sequences of Group Representations. I. Algebras and Representation Theory 1, 97–127 (1998). https://doi.org/10.1023/A:1009968402535
Issue Date:
DOI: https://doi.org/10.1023/A:1009968402535