A Jacobson Radical Decomposition of the Fano-Snowflake Configuration

Details A Jacobson Radical Decomposition of the Fano-Snowflake Configuration A Jacobson Radical Decomposition of the Fano-Snowflake Configuration

2008-07-11

arxiv.org/abs/0807.1790v2

SIGMA 4 (2008) 072, 7 pages

Physics

Mathematical Physics

7 pages, 3 figures

Scientific paper

10.3842/SIGMA.2008.072

The Fano-Snowflake, a specific $non$-unimodular projective lattice configuration associated with the smallest ring of ternions $R_{\diamondsuit}$ (arXiv:0803.4436 and 0806.3153), admits an interesting partitioning with respect to the Jacobson radical of $R_{\diamondsuit}$. The totality of 21 free cyclic submodules generated by non-unimodular vectors of the free left $R_{\diamondsuit}$-module $R_{\diamondsuit}^{3}$ are shown to split into three disjoint sets of cardinalities 9, 9 and 3 according as the number of Jacobson radical entries in the generating vector is 2, 1 or 0, respectively. The corresponding "ternion-induced" factorization of the lines of the Fano plane sitting in the middle of the Fano-Snowflake (6 -- 7 -- 3) is found to $differ fundamentally$ from the natural one, i. e., from that with respect to the Jacobson radical of the Galois field of two elements (3 -- 3 -- 1).

Affiliated with

Also associated with

No associations

Rating

A Jacobson Radical Decomposition of the Fano-Snowflake Configuration does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Jacobson Radical Decomposition of the Fano-Snowflake Configuration, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Jacobson Radical Decomposition of the Fano-Snowflake Configuration will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-575664