In this paper, by calculating the commutator subgroup of the unit group of finite path algebra k∆ and the unit group abelianized, we explicitly characterize the K1 group of finite dimensional path algebra over an arbitrary field.

Let k be an algebraically closed field of characteristic p > 0. The purpose of this paper is to describe the Hopf algebra of a finite commutative infinitesimal unipotent k-group scheme which is uniserial, i.e., which has a unique composition series. As there is only one simple finite commutative infinitesimal unipotent group scheme (namely αp := ker {F : Ga → Ga} , with Ga being the additive gr...

Let H be a Hopf algebra with a bijective antipode over a commutative ring k with unit. The Brauer group of H is defined as the Brauer group of Yetter–Drinfel’d H-module algebras, which generalizes the Brauer–Long group of a commutative and cocommutative Hopf algebra and those known Brauer groups of structured algebras.

In the paper, we describe the teleportation from the viewpoints of the braid group and Temperley–Lieb algebra. We propose the virtual braid teleportation which exploits the teleportation swapping and identifies unitary braid representations with universal quantum gates, and further suggest the braid teleportation which is explained in terms of the crossed measurement and the state model of knot...

g∈G agg −1 is an antiautomorphism of KG of order 2. An element v of V (KG) satisfying v = v is called unitary. We denote by V∗(KG) the subgroup of V (KG) formed by the unitary elements of KG. Let char(K) be the characteristic of the field K. In [2], A.Bovdi and A. Szákacs construct a basis for V∗(KG) where char(K) > 2. Also A. Bovdi and L. Erdei [1] determine the structure of V∗(F2G) for all gr...