Bodo Pareigis

  • Citations Per Year
Learn More
The category of Yetter-Drinfeld modules YD K over a Hopf algebra K (with bijektive antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YD K such that the set of primitive(More)
Sequential dynamical systems have the property, that the updates of states of individual cells occur sequentially, so that the global update of the system depends on the order of the individual updates. This order is given by an order on the set of vertices of the dependency graph. It turns out that only a partial suborder is necessary to describe the(More)
The category of group-graded modules over an abelian group G is a monoidal category. For any bicharacter of G this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have n-ary multiplications between various graded components.(More)
The theory of Hopf algebras is closely connected with various applications, in particular to algebraic and formal groups. Although the rst occurence of Hopf algebras was in algebraic topology, they are now found in areas as remote as combinatorics and analysis. Their structure has been studied in great detail and many of their properties are well(More)
In this paper we introduce left linear theories of exponent N (a set) on the set L as maps L L 3 (l; ) ! l 2 L such that for all l 2 L and ; 2 L the relation (l ) = l( ) holds, where 2 L is given by ( )(i) = (i) ; i 2 N . We assume that L has a unit, that is an element 2 L with l = l, for all l 2 L, and = , for all 2 L . Next, left (resp. right) L-modules(More)