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On the Wood bases of a Steenrod algebra mod pстатья
- Автор: Emelyanov D.Yu
- Журнал: Fundam. Prikl. Mat
- Том: 20
- Номер: 3
- Год издания: 2015
- Первая страница: 83
- Последняя страница: 90
- Аннотация: Let p be an odd prime and let A_p be the mod p Steenrod algebra. Denote by \bar{A}_p the subalgebra of A_p generated by the cohomology operations P^j, j⩾0, and let \bar{Z}^n_k=P^{p^k+p^{k+1}+⋯+p^n} with 0⩽k⩽n. The monomial \bar{Z}^{n_0}_{k_0}\bar{Z}^{n_1}_{k_1}⋯\bar{Z}^{n_r}_{k_r} is called a WY-monomial if the sequence of pairs I=((k_0,n_0),(k_1,n_1),…,(k_r,n_r)) satisfies certain conditions. The main result of this paper is that the set of WY-monomials is a basis of \bar{A}_p for an odd prime p. The author defines the WZ-monomials in A_p and observes that the set of WZ-monomials is also a basis of \bar{A}_p for an odd prime p. The results of this paper generalize the ones of R. M. W. Wood for the Steenrod algebra A_2 [Bull. London Math. Soc. 27 (1995), no. 4, 380–386; MR1335290].
- Добавил в систему: Емельянов Данила Юрьевич