UTA Department of Mathematics

Algebra Seminar

Date/Time/Room: Friday (09/17/2004) at 4:00pm in 487 Pickard Hall

Speaker: Kristen Beck, Department of Mathematics, University of Texas at Arlington

"The Category of Complexes, Part II"

Abstract: We will begin this talk by defining the tensor product of (1) graded R-modules and (2) their morphisms, and will see that these constructions induce a functor from GM(R) x GM(R) into GM(R). Viewing a complex as a graded R-module together with a differential, we will then be equipped to define the tensor product of complexes of R-modules. These tensors will then help to induce a functor from DGM(R) x DGM(R) into DGM(R), which will commute with the aforementioned forgetful functor. Several canonical isomorphisms, including the transposition of the tensor product of two complexes, and an expression for the shift automorphism, will be mentioned. Time permitting, we will proceedto investigate homomorphisms of complexes.