We complete the construction of the biassociahedra , construct the free matrad , realize as the cellular chains of , and define an -bialgebra as an algebra over . We construct the bimultiplihedra , construct the relative free matrad as a -bimodule, realize as the cellular chains of , and define a morphism of -bialgebras as a bimodule over . We prove that the homology of every -bialgebra over a commutative ring with unity admits an induced -bialgebra structure. We extend the Bott-Samelson isomorphism to an isomorphism of -bialgebras and determine the -bialgebra structure of . For each , we construct a space and identify an induced nontrivial -bialgebra operation .
*This research was funded in part by grant SRNSF/217614 and multiple Millersville University Research Grants.
The current pdf replaces the original pdf file, first available on 22 December 2022. The new version corrects the DOI prefix to read 10.32513.
The second author wishes to thank the Institute of Mathematics of the Czech Academy of Sciences and the Institute of Mathematics of University of Seville (IMUS) for providing financial support and residential accommodations during various stages of this project.
Samson Saneblidze. Ronald Umble. "Framed Matrices and -Bialgebras *." Adv. Studies: Euro-Tbilisi Math. J. 15 (4) 41 - 140, December 2022. https://doi.org/10.32513/asetmj/19322008230