Basic quantum algebra
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911058119098368 |
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| author | Banica, Teo |
| author_facet | Banica, Teo |
| contents | This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields $F$. These algebras $A$ satisfy a commutativity type condition, and the general idea is that of lifting this condition, and calling quantum spaces the underlying space-like objects $X$. One problem comes from the fact that different fields $F$ lead, via different algebras $A$, to different classes of quantum spaces $X$. Our aim here is to identify and put at the center of the presentation those quantum spaces $X$ which do not depend on the choice of $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11459 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Basic quantum algebra Banica, Teo Quantum Algebra Rings and Algebras Representation Theory This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields $F$. These algebras $A$ satisfy a commutativity type condition, and the general idea is that of lifting this condition, and calling quantum spaces the underlying space-like objects $X$. One problem comes from the fact that different fields $F$ lead, via different algebras $A$, to different classes of quantum spaces $X$. Our aim here is to identify and put at the center of the presentation those quantum spaces $X$ which do not depend on the choice of $F$. |
| title | Basic quantum algebra |
| topic | Quantum Algebra Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2507.11459 |