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Physical role of v-invariants in SU(2) (m) × L8 dual mappings over {H̃v} carrier spaces for Liouville multiple-quantum NMR of spin clusters within Ln-automorphisms: [13CH]8, [−2D]8-cubanes and some SU(6) aspects of a [Ti]8[13C]+12-met-carb

Author

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  • Colpa, J.P.
  • Temme, F.P.

Abstract

The nature of [A]8 MQ-NMR spin clusters and their NMR structure within cooperative (non-shell) dual mapping over carrier subspaces {H̃v} of Liouville space is examined in the context of the dual-group symmetry-chain and inner tensor product (ITP) algebras. The v-recoupling terms of {G̃G(v)}, conveniently realised as number partitions (NP) which identity the distinct carrier subspaces, are shown to play a fundamental role as Rota scalar-invariants-over-a-field in the mechanism of SU2-to-Ln cooperativity. These quasi-invariants (number partitions) from v parallel the sets of Ln-irreps (chain subduced L8 ↓ L6 ↓ O irreps) which allow for the block-partioning of the information-rich higher-q multiple quantum aspects of MQ-NMR. The specific value of mathematical physics of induced (subduced) Ln groups, ITPs and Ln-invariant p-tuple (NP) models, is demonstrated for the MQ-NMR both of cubanes, under SU2(3) × L8 ↓ L6 ↓ O, and of a [Ti]8−[C]12 met-carb cation under SU(6) × L8.

Suggested Citation

  • Colpa, J.P. & Temme, F.P., 1994. "Physical role of v-invariants in SU(2) (m) × L8 dual mappings over {H̃v} carrier spaces for Liouville multiple-quantum NMR of spin clusters within Ln-automorphisms: [13CH]8, [−2D]8-cubanes and some SU," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 209(1), pages 140-161.
    • Handle: RePEc:eee:phsmap:v:209:y:1994:i:1:p:140-161
    DOI: 10.1016/0378-4371(94)90054-X
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