Lothar Gerritzen

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Generalizations of the series exp and log to noncommutative non-associative and other types of algebras were regarded by M. Lazard, and recently by V. Drensky and L. Gerritzen. There is a unique power series exp(x) in one non-associative variable x such that exp(x) exp(x) = exp(2x), exp ′ (0) = 1. We call the unique series H = H(x, y) in two non-associative(More)
In this note we introduce the concept of a shuffle product ⊔⊔ for planar tree polynomials and give a formula to compute the planar shuffle product S ⊔⊔ T of two finite planar reduced rooted trees S, T. It is shown that ⊔⊔ is dual to the co-addition ∆ which leads to a formula for the coefficients of ∆(f). It is also proved that ∆(EXP) = EXPˆ⊗EXP where EXP is(More)
The notion of binomial coefficients T S of finite planar, reduced rooted trees T, S is defined and a recursive formula for its computation is shown. The nonassociative binomial formula (1 + x) T = S T S x S for powers relative to T is derived. Similarly binomial coefficients T S,V of the second kind are introduced and it is shown that (x ⊗ 1 + 1 ⊗ x) T =(More)
Acknowledgments First of all it is a pleasure to thank my supervisor Hans Ulrich Simon for the great support and the nice atmosphere in his research group. He has been a reliable source of encouragement and adv ice through all my years at the Ruhr-Universität Bochum. Thanks also to all the nice people I met at the " Lehrstuhl für Mathematik und Informatik "(More)
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