Dihedral homology and homotopy fixed point sets

Adams and Steenrod operators in dihedral homology

“…where P 0 if < 0, and if q 2j , where e 0 or 1, then '7( q) 1 Now we prove the main second theorem in this work. THEOREM 2.2.…”

“…Note that, in general, the permutation gj of the ordered set O, 1 Note that the decreasing (by one) of the elements in the set {0,1, n} met the increasing of elemems (also by one) in the set {n,n-1 ,0}. Suppose that the arguments of the summation in (1 2) correspond to the permutation aI.…”

“…The dihedral (co)homology of unital algebra with an involution, symmetry, bisymmetry and Weile has been studied by Looder [1 ], Krasauskas, Lapin and Solovev [2], Kolosov [3] and others In the present work we are concerned with Adam's and Steenrod's operators in the dihedral homology.…”

Reflexive and dihedral (co)homology of a pre‐additive category

“…The category ∆Ᏸ is called a dihedral category. Note that the category generated by only the morphisms δ i n and σ j n is called a simplicial category and is denoted by ∆, the category generated by δ i n , σ j n , and τ n is a cyclic category and is denoted by ∆C (see [6]), and the category generated by the family of morphisms δ i n , σ j n , and ρ n is called a reflexive category and is denoted by ∆R. Definition 1.2 (see [3]).…”

The relative dihedral homology of involutive algebras

“…First, we recall some definitions and facts from [4,5]. Let A be an associative algebra over a field k(k = R or C).…”