ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXV, 1 (2006)
p. 21 - 30

The Frobenius theorem on N-dimensional quantum hyperplane
C. Ciupala

Abstract. In this paper we introduce the universal r -differential calculus on a r -algebra and we prove the universality of the construction. We also present submanifolds, distributions, linear connections and two different r -differential calculi on S_N^q: the algebra of forms and the algebra of universal differential forms of S_N^q. Finally we prove the Frobenius theorem on the N-dimensional quantum hyperplane S_N^q in a general case, for any r -differential calculus on S_N^q.

Keywords: Noncommutative geometry, linear connections, submanifolds, distributions, quantum hyperplane.

AMS Subject classification: 81R60, 16W99, 53C04.

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Acta Mathematica Universitatis Comenianae
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