On the Construction of a Groupoid from an Ample Hausdorff Groupoid with Twisted Steinberg Algebra not Isomorphic to its Non-twisted Steinberg Algebra
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i1.5051Keywords:
Groupoids, Steinberg Algebra, Twisted Steinberg Algebra, Non-twisted Steinberg AlgebraAbstract
This study introduces an ample Hausdorff groupoid $\hat{A} \rtimes \mathcal{R}$ extracted from an ample Hausdorff groupoid $\mathcal{G}$ and a unital commutative ring $R$; a Hausdorff groupoid $D$ which is the discrete twist over $\hat{A} \rtimes \mathcal{R}$. In the groupoid C*-algebra perspective, when $R = \mathbb{C}$ there is an isomorphism between the non-twisted groupoid C*-algebra $(C^*(\mathcal{G}))$ and the twisted groupoid C*-algebra $(C^*(\hat{A} \rtimes \mathcal{R};D))$. However, in this paper, in a purely algebraic setting, the non-twisted Steinberg algebra $(A_R(\mathcal{G}))$ and the twisted Steinberg algebra $(A_R(D; \hat{A} \rtimes \mathcal{R}))$ are non-isomorphic.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 European Journal of Pure and Applied Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.
By agreeing to this statement, you acknowledge that:
- You retain full copyright over your work.
- The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
- This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.