Isomorphisms between Subiaco {$q$}-clan geometries

Isomorphisms Between Subiaco q–Clan Geometries

For q = 2e, e ≥ 4, the Subiaco construction introduced in [2] provides one q–clan, one flock, and for e 6≡ 2 (mod 4), one oval in PG(2, q). When e ≡ 2 (mod 4), there are two inequivalent ovals. The associated generalised quadrangle of order (q, q) has a complete automorphism group G of order 2e(q − 1)q. For each Subiaco oval O there is a group of collineations of PG(2, q) induced by a subgroup ...

Isomorphisms between Quantum Group Covariant q - Oscillator Systems Defined for q and q − 1

It is shown that there exists an isomorphism between q-oscillator systems covariant under SUq(n) and SUq−1(n). By the isomorphism, the defining relations of SUq−1(n) covariant q-oscillator system are transmuted into those of SUq(n). It is also shown that the similar isomorphism exists for the system of q-oscillators covariant under the quantum supergroup SUq(n/m). Furthermore the cases of q-def...

The Fundamental Theorem of q-Clan Geometry

Some Isomorphisms Between Functor Categories

The scheme ChoiceD concerns a non-empty set A, a non-empty set B, and a binary predicate P, and states that: there exists a function h from A into B such that for every element a of A holds P[a, h(a)] provided the parameters meet the following requirement: • for every element a of A there exists an element b of B such that P[a, b]. Let A, B, C be non-empty sets, and let f be a function from A i...

Weak isomorphisms between Bernoulli shifts

In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.