Abstract
Consideration ofL n groups for n even and between 6 ≤n:≤ 20, (60) is consistent with the existence (over a simply reducible (SR) space) of certain similarities in the inner tensor product (ITP) structures associated with -p ≤ 2 [n -1, 1] ⊗ [λ.], or -⊗ [(n/2)2] products, and for general (even)n for [n -1, 1] ⊗ [n - 2, 12] ITPs, but not for ITPs involving higher generalm (p ≤ 3) components, as in [n-1, 1] ⊗ [n-m, m-1, 1].These observations provide considerable insight into the nature of van der Waals (3 ≤ n ≤ 20), metallic-, or “met-carb-” clusters andn = 12, 20 cage molecules analogous to dodecahedrane (a cage,n = 20 molecule) or13C buckminsterfullerene(ane) (n = 60) [A] n , [AX] n clusters, besides allowing for further combinatorial views on higherL n group characters and their associated group algebra. Mathematical insight to date into the nature of general ITPs involvingnon-SR direct sums has proved less fruitful on account of the number of component partitions spanned by specific TTP maps and their associated multiplicities.
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Temme, F.P. On general forms for structure of some [n−1, 1] ⊗ [λ]L n n inner tensor products with 6 ≤n≤ 20, (60) forn even, in the context of spin cluster problems of multiquantum NMR. J Math Chem 13, 153–165 (1993). https://doi.org/10.1007/BF01165561
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DOI: https://doi.org/10.1007/BF01165561