[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2014.29.3.463

CRITERIA FOR A SYMMETRIZED MONOMIAL IN B(3) TO BE NON-HIT

Janfada, Ali S. (Department of Mathematics Urmia University)

Publication Information

Communications of the Korean Mathematical Society / v.29, no.3, 2014 , pp. 463-478 More about this Journal

Abstract

We find criteria for symmetrized monomials to be non-hit in the $\mathcal{A}_2$ -algebra of symmetric polynomials in three variables, where $\mathcal{A}_2$ is the mod 2 Steenrod algebra.

Keywords

hit problem; symmetric hit problem; Steenrod algebra;

Citations & Related Records

Reference

1	D. P. Carlisle and R. M. W. Wood, The boundedness conjecture for the action of the Steenrod algebra on polynomials, Adams Memorial Symposium on Algebraic Topology, 2 (Manchester, 1990), 203-216, London Math. Soc. Lecture Note Ser., 176, Cambridge Univ. Press, Cambridge, 1992.
2	A. S. Janfada, A criterion for a monomial in P(3) to be hit, Math. Proc. Cambridge Philos. Soc. 145 (2008), no. 3, 587-599. DOI ScienceOn
3	A. S. Janfada, On a conjecture on the symmetric hit problem, Rend. Circ. Mat. Palermo 60 (2011), no. 3, 403-408. DOI
4	A. S. Janfada and R. M. W. Wood, The hit problem for symmetric polynomials over the Steenrod algebra, Math. Proc. Cambridge Philos. Soc. 133 (2002), no. 2, 295-303.
5	A. S. Janfada and R. M. W. Wood, Generating H*(BO(3), $F_2$ ) as a module over the Steenrod algebra, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 2, 239-258. DOI ScienceOn
6	M. Kameko, Generators of the cohomology of $BV_3$ , J. Math. Kyoto Univ. 38 (1998), no. 3, 587-593. DOI
7	F. P. Peterson, A-generators for certain polynomial algebras, Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 311-312. DOI
8	N. Sum, The hit problem for the polynomial algebra of four variables, Seoul, November 3, (2007), http://www.kms.or.kr/data/asia/files/nguyensum.pdf
9	N. Sum, The negative answer to Kameko's conjecture on the hit problem, Adv. Math. 225 (2010), no. 5, 2365-2390. DOI ScienceOn
10	A. S. Janfada, The Hit Problem for Symmetric Polynomials Over the Steenrod Algebra, PhD thesis, Manchester University, UK, 2000.
11	L. Smith, Polynomial Invariants of Finite Groups, Res. Notes Math., vol. 6, A. K. Peters Ltd. Wellesley, MA, 1995.