Heaps and trusses

Abstract: I will present the first notions concerning heaps and trusses. Heaps were introduced for the first time by H. Prüfer (1924) and R. Baer (1929). A heap is a pair $(H, [−,−,−])$ consisting of a set $H$ and a ternary operation $$[−,−,−] : H \times H \times H \to H, (x, y, z)  \to [x, y, z],$$ such that, for all $v, w, x, y, z \in H,$ $$[v, w, [x, y, z]] = [[v, w, x, ], y, z], \ [x, x, y] = y,\ [y, x, x]= y.$$ Truss is a much more recent algebraic structure (T. Brzeziński, 2019). A truss is a heap with a further associative binary operation, denoted by juxtaposition, which distributes over $[−,−,−],$ that is, for all $w, x, y, z \in T,$ $$w[x, y, z] = [wx, wy, wz], \ [x, y, z]w = [xw, yw, zw],\ [x, y, z] =[z, y, x].$$

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar