caa a22 4500 445835656 CHVBK 20180317145329.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00209-010-0697-2 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0697-2 Graph products of spheres, associative graded algebras and Hilbert series [Elektronische Daten] [Peter Bubenik, Leah Gold] Given a finite, simple, vertex-weighted graph, we construct a graded associative (noncommutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to edges. We show that the Hilbert series of this algebra is the inverse of the clique polynomial of the graph. Using this result it easy to recognize if the ideal is inert, from which strong results on the algebra follow. Noncommutative Gröbner bases play an important role in our proof. There is an interesting application to toric topology. This algebra arises naturally from a partial product of spheres, which is a special case of a generalized moment-angle complex. We apply our result to the loop-space homology of this space. Springer-Verlag, 2010 Bubenik Peter Department of Mathematics, Cleveland State University, 44115-2214, Cleveland, OH, USA aut Gold Leah Department of Mathematics, Cleveland State University, 44115-2214, Cleveland, OH, USA aut Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 821-836 0025-5874 268:3-4<821 2011 268 209 https://doi.org/10.1007/s00209-010-0697-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0697-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bubenik Peter Department of Mathematics, Cleveland State University, 44115-2214, Cleveland, OH, USA aut NATIONALLICENCE 700 1- Gold Leah Department of Mathematics, Cleveland State University, 44115-2214, Cleveland, OH, USA aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/3-4(2011-08-01), 821-836 0025-5874 268:3-4<821 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer