Differential Systems Associated with Tableaux over Lie Algebras
نویسندگان
چکیده
We give an account of the construction of exterior differential systems based on the notion of tableaux over Lie algebras as developed in [33]. The definition of a tableau over a Lie algebra is revisited and extended in the light of the formalism of the Spencer cohomology; the question of involutiveness for the associated systems and their prolongations is addressed; examples are discussed.
منابع مشابه
Tableaux over Lie algebras, integrable systems and classical surface theory
Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical soliton surfaces. Completely integrable equations such as the G/G0-system of Terng...
متن کاملar X iv : m at h / 04 12 16 9 v 1 [ m at h . D G ] 8 D ec 2 00 4 TABLEAUX OVER LIE ALGEBRAS , INTEGRABLE SYSTEMS , AND CLASSICAL SURFACE THEORY
Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, projective minimal surfaces, and other classical soliton surfaces. Completely integrable equations suc...
متن کاملar X iv : m at h / 04 12 16 9 v 3 [ m at h . D G ] 2 A ug 2 00 6 TABLEAUX OVER LIE ALGEBRAS , INTEGRABLE SYSTEMS , AND CLASSICAL SURFACE THEORY
Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical soliton surfaces. Completely integrable equations such as the G/G0-system of Terng...
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