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Статья «NONCOMMUTATIVE HOLOMORPHIC FUNCTIONAL CALCULUS, AFFINE AND PROJECTIVE SPACES FROM NC-COMPLETE ALGEBRAS, "Алгебра и анализ"»

Авторы:
  • DOSI A.1
стр. 48-113
Платно
1 Middle East Technical University
  • SDI: 007.001.0234-0852.2019.031.004.3
Аннотация:
The paper is devoted to a noncommutative holomorphic functional calculus and its application to noncommutative algebraic geometry. A description is given for the noncommutative (infinite-dimensional) affine spaces A, 1 ? q ? ?, x =(x)i?, and for the projective spaces P within Kapranov’s model of noncommutative algebraic geometry based on the sheaf of formally-radical holomorphic functions of elements of a nilpotent Lie algebra and on the related functional calculus. The obtained result for q = ? generalizes Kapranov’s formula in the finite dimensional case of A. The noncommutative scheme P corresponds to the graded universal enveloping algebra U (g (x)) of the free nilpotent Lie algebra of index q generated by x = (x,... ,x) with deg (x) = 1, 0 ? i ? n. A sheaf construction B (P, fq, O (-2),..., O (-q)) is suggested, in terms of the twisted sheaves O (-2),..., O (-q) on P and the formal power series fq, to restore the coordinate ring of P which is reduced to U (g (x)). Finally, the related cohomology groups H (P, O (d)), i ? 0, are calculated.

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