Pith. Sign in

RECORD

Z_2-gradings of Clifford algebras and multivector structures

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Ricardo A. Mosna, David Miralles, Jayme Vaz Jr

Mathematical Physics · Submitted 5 Dec 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath-ph/0212020 (version 2)
Pith IDRCA7D6ZM, Pith's permanent record of this paper and its review
CitationDavid Miralles, Jayme Vaz Jr, Ricardo A. Mosna. "Z_2-gradings of Clifford algebras and multivector structures." arXiv:math-ph/0212020 (2002). https://pith.science/paper/RCA7D6ZM
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,270 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. background 1.00 0.07 0.02 asserted 0.89
s1 In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. contribution 0.98 0.81 0.07 asserted 0.86
s2 A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. result 0.78 0.95 0.64 asserted 1.00
s3 An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. result 0.95 0.94 0.11 asserted 1.00
s4 Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra. contribution 0.93 0.94 0.28 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure of the Grassmann algebra over V. A complete characterization for such Z_2-gradings is obtained by classifying all the even subalgebras coming from them. An expression relating such subalgebras to the usual even part of Cl(V,g) is also obtained. Finally, we employ this framework to define spinor spaces, and to parametrize all the possible signature changes on Cl(V,g) by Z_2-gradings of this algebra.

Human review

How Pith checks papers → · Full audit of this paper →

References
How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.