SUBALGEBRAS OF GOLOD–SHAFAREVICH ALGEBRAS
2009 ◽
Vol 19
(03)
◽
pp. 423-442
◽
A graded associative algebra generated by m elements of degree one is called Golod–Shafarevich (GS) if it is presented with less than m2/4 relators of degree at least two. We explore conditions under which subalgebras of graded GS algebras are themselves GS. We prove that infinitely many Veronese powers of an algebra presented by m generators and r relators are GS if [Formula: see text]. For quadratic algebras, the bound is improved to [Formula: see text]. We also show that if A is a generic quadratic algebra presented by m generators and r relators, then all Veronese powers of A are GS if [Formula: see text], and all but finitely many Veronese powers of A are not GS if [Formula: see text].
2014 ◽
Vol 29
(06)
◽
pp. 1450028
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2014 ◽
Vol 12
(05)
◽
pp. 583-612
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2006 ◽
Vol 136
(4)
◽
pp. 717-731
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1992 ◽
Vol 52
(2)
◽
pp. 154-174
2017 ◽
Vol 60
(2)
◽
pp. 361-399
◽
Keyword(s):
2011 ◽
Vol 328
(1)
◽
pp. 287-300
◽
1992 ◽
Vol 07
(supp01b)
◽
pp. 773-779
◽
Keyword(s):