{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:36:12Z","timestamp":1760236572123,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,6]],"date-time":"2021-12-06T00:00:00Z","timestamp":1638748800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We introduce a quantum model for the universe at its early stages, formulating a mechanism for the expansion of space and matter from a quantum initial condition, with particle interactions and creation driven by algebraic extensions of the Kac\u2013Moody Lie algebra e9. We investigate Kac\u2013Moody and Borcherds algebras, and we propose a generalization that meets further requirements that we regard as fundamental in quantum gravity.<\/jats:p>","DOI":"10.3390\/sym13122342","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T02:48:13Z","timestamp":1638845293000},"page":"2342","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Space, Matter and Interactions in a Quantum Early Universe Part I: Kac\u2013Moody and Borcherds Algebras"],"prefix":"10.3390","volume":"13","author":[{"given":"Piero","family":"Truini","sequence":"first","affiliation":[{"name":"Istituto Nazionale Fisica Nucleare (INFN) , Sez. di Genova, Via Dodecaneso 33, I-16146 Genova, Italy"},{"name":"Quantum Gravity Research (QGR), 101 S. Topanga Canyon Rd., 1159, Los Angeles, CA 90290, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7597-1050","authenticated-orcid":false,"given":"Alessio","family":"Marrani","sequence":"additional","affiliation":[{"name":"Centro Studi e Ricerche Enrico Fermi, Via Panisperna 89A, I-00184 Roma, Italy"}]},{"given":"Michael","family":"Rios","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research (QGR), 101 S. Topanga Canyon Rd., 1159, Los Angeles, CA 90290, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2938-3941","authenticated-orcid":false,"given":"Klee","family":"Irwin","sequence":"additional","affiliation":[{"name":"Quantum Gravity Research (QGR), 101 S. Topanga Canyon Rd., 1159, Los Angeles, CA 90290, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,6]]},"reference":[{"key":"ref_1","unstructured":"Truini, P., Marrani, A., Rios, M., and Irwin, K. (2012). Space, Matter and Interactions in a Quantum Early Universe. 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