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Hopf algebra polynomial identities in the Sweedler algebra
Abstract
Using Mac Lane's PROPs, one can introduce multilinear polynomial identities that involve all the operations of a Hopf algebra: the (co)multiplication, the (co)unit and the antipode. We find bases for polynomial identities and calculate their codimensions for the Sweedler algebra, treating it first as an ordinary associative algebra over a field and second as a Hopf algebra.
Related
BibTeX
@misc{gordienko2026hopf,
title = {{Hopf algebra polynomial identities in the Sweedler algebra}},
author = {Alexey Gordienko and Maria Morozova},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05187},
eprint = {2611.05187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05187},
}
RIS
TY - UNPB
TI - Hopf algebra polynomial identities in the Sweedler algebra
AU - Alexey Gordienko
AU - Maria Morozova
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05187
UR - https://arxiv.org/abs/2611.05187
AB - Using Mac Lane's PROPs, one can introduce multilinear polynomial identities that involve all the operations of a Hopf algebra: the (co)multiplication, the (co)unit and the antipode. We find bases for polynomial identities and calculate their codimensions for the Sweedler algebra, treating it first as an ordinary associative algebra over a field and second as a Hopf algebra.
ER -