منابع مشابه
Antipodes and involutions
If H is a connected, graded Hopf algebra, then Takeuchi’s formula can be used to compute its antipode. However, there is usually massive cancellation in the result. We show how sign-reversing involutions can sometimes be used to obtain cancellationfree formulas. We apply this idea to the Hopf algebras of polynomials, graphs, and noncommutative symmetric functions.
متن کاملDualizations and Antipodes
Abstract Because an exact pairing between an object and its dual is extraordinarily natural in the object, ideas of the paper [St4] apply to yield a definition of dualization for a pseudomonoid in any autonomous monoidal bicategory as base; this is an improvement on [DS; Definition 11, page 114]. We analyse the dualization notion in depth. An example is the concept of autonomous (which, usually...
متن کاملGoal-directed control and its antipodes
In instrumental conditioning, there is a rather precise definition of goal-directed control, and therefore an acute boundary between it and the somewhat more amorphous category comprising its opposites. Here, we review this division in terms of the various distinctions that accompany it in the fields of reinforcement learning and cognitive architectures, considering issues such as declarative a...
متن کاملBioclimatic Zones for the Antipodes - and Beyond?
Introduction Bioclimatic zone systems aim to define reproducible sets of named biogeographical cells that facilitate global comparisons of ecological data. Zones based on extant vegetation loosely reflect contemporary climate, but are vitiated by climate history, chance establishment, genetic potential of local species, terrain instability, intrazonal soils, and biotic disturbance. The system o...
متن کاملGauge Invariants from the Powers of Antipodes
We prove that the trace of the nth power of the antipode of a Hopf algebra with the Chevalley property is a gauge invariant, for each integer n. As a consequence, the order of the antipode, and its square, are invariant under Drinfeld twists. The invariance of the order of the antipode is closely related to a question of Shimizu on the pivotal covers of finite tensor categories, which we affirm...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2017
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2016.12.005