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- BY CHARLES W. CURTIS, Charles W. Curtis
- 2007

The representation theory of a group G over the field of complex numbers involves two problems: first, the construction of the irreducible representations of G; and second, the problem of expressing each suitably restricted complex valued function on G, as a linear combination (or a limit of linear combinations), of the coefficients of the irreducible… (More)

Let £ be a split semisimple Lie algebra over a field <E> of characteristic zero and <£ = 3C+ ]C«eA«£a be the rootspace decomposition of <£ relative to a splitting Cartan subalgebra 5C, where the subset A of 3C* is the corresponding root-system. Fix a simple system of roots {c*i, «2, • • • , ai}, for which the positive (resp. negative) roots are denoted by… (More)

- FINITE GROUPS, Charles W. Curtis
- 2010

Introduction. In this paper it is proved that the irreducible projective representations of the group G of automorphisms of a Lie algebra of classical type constructed in [2] remain irreducible and inequivalent when restricted to the subgroup Go of G generated by the oneparameter subgroups {exp(ad£ea)} where a ranges over the set of roots of ? with respect… (More)

Introduction. I t is known [13] that a Lie algebra over a modular field has indecomposable representations of arbitrarily high dimensionalities. If, however, the Lie algebra and its representations are required to be restricted (see [6, Chapter 5] for definitions), this need no longer be the case. A restricted Lie algebra for which the degrees of its… (More)

- Eldon Dyer, R. Creighton Buck, +94 authors Bodo Pareigis
- 2010

240. 9. B. Pareigis and A . Rosenberg, Addendum to Amitsur's complex f o r p u r e l y i n separable fields," Osaka Math. J . (to appear). CORNELL UNIVERSITY AND UNIVERSITÄT HEIDELBERG

- Charles W. Curtis
- The American Mathematical Monthly
- 2003

1. Introduction. We shall say that an integral domain1 R satisfies condition (M) if any two nonzero elements of R have a nonzero common right multiple. In this note it is proved that if 5 is an extension of a ring R such that S is, roughly speaking, a noncommutative polynomial ring in one variable with R as a coefficient ring, and if R has the property (M),… (More)

- Carla Bardini, C. Bardini, Charles W. Curtis, Nagayoshi Iwahori, Nikolai Vavilov
- 2013

This paper is about some graph isomorphisms between the Auslander-Reiten quivers of the path algebras of quivers with underlying Dynkin diagrams of type Al, and the weight diagrams or the weight graphs relative to some basic (adjoint) representations of a semi-simple complex Lie algebra associated to the same Dynkin diagrams. The crucial point is that, in… (More)

- Nathan A. Jacobson, Wei-Liang Chow, +21 authors Catherine Chevalley
- 2007

The First Summer Mathematical Institute, devoted to Lie algebras and Lie groups, was held from June 20 to July 31, 1953 at Colby College, Waterville, Maine. It was supported by a grant from the National Science Foundation to the American Mathematical Society. The Organization Committee consisted of C. C. Chevalley, A. M. Gleason, and Nathan Jacobson… (More)