منابع مشابه
Generalized Heisenberg Algebras and Fibonacci Series
We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliar operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by Fibonacci sequence. Moreover, the algebraic structure depends on tw...
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We prove that free pre-Lie algebras, when considered as Lie algebras, are free. Working in the category of S-modules, we define a natural filtration on the space of generators. We also relate the symmetric group action on generators with the structure of the anticyclic PreLie operad.
متن کاملFree Algebras in Varieties
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility. In universal algebra we deal with varieties – classes o...
متن کاملAlmost Free Algebras
In this paper we adopt the terminology of universal algebra. So by a free algebra we will mean that a variety (i.e., an equationally defined class of algebras) is given and the algebra is free in that variety. We will also assume that the language of any variety is countable. In this paper the investigation of the almost free algebras is continued. An algebra is said to be almost free if “most”...
متن کاملRepresenting free Boolean algebras
Partitioner algebras are defined in [2] and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in [2] by showing that the free algebra with א1 generators is represented. It w...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1989
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700004342