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arXiv · 2412.04612

The criteria for the uniqueness of a weight homomorphism of a baric algebra

Dali Zangurashvili
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Abstract

The criteria for a baric algebra $A$ (over a field $K$) to have a unique weight homomorphism are found. One of them requires a certain system of equations to have a unique non-trivial solution in the field $K$. Applying this criterion, we provide an example showing that Holgate's well-known sufficient condition for the uniqueness of a weight homomorphism is not necessary, and give also a new example of a baric algebra with two weight homomorphisms. Another criterion found in this paper asserts that a baric algebra has a unique weight homomorphism if and only if the transition matrix from any semi-natural basis $B_1$ to any semi-natural basis $B_2$ is stochastic.

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Dali Zangurashvili. 2024-12-05. The criteria for the uniqueness of a weight homomorphism of a baric algebra. https://arxiv.org/abs/2412.04612

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