MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 605-611, 2002

The integrability of a field of endomorphisms

Gerard Thompson

Gerard Thompson, Department of Mathematics, The University of Toledo, Toledo, Ohio 43606, U.S.A., e-mail: gthompson@uoft02.utoledo.edu

Abstract: A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.

Keywords: integrability, endomorphism, quotient space

Classification (MSC 2000): 53C10, 53C15, 53A35

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