Trees, free right-symmetric algebras, free Novikov algebras and identities
نویسندگان
چکیده
منابع مشابه
The Freiheitssatz and the Automorphisms of Free Right-symmetric Algebras
We prove the Freiheitssatz for right-symmetric algebras and the decidability of the word problem for right-symmetric algebras with a single defining relation. We also prove that two generated subalgebras of free right-symmetric algebras are free and automorphisms of two generated free right-symmetric algebras are tame. Mathematics Subject Classification (2000): Primary 17A36, 17A50; Secondary 1...
متن کاملFree Rota – Baxter Algebras and Rooted Trees
A Rota–Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota–Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota–Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota–Baxter algebras were obtained by Rota and Cartier in the 1970s and a third ...
متن کاملFermionic Novikov Algebras Admitting Invariant Non-degenerate Symmetric Bilinear Forms Are Novikov Algebras
Gelfand and Dikii gave a bosonic formal variational calculus in [5, 6] and Xu gave a fermionic formal variational calculus in [13]. Combining the bosonic theory of Gelfand-Dikii and the fermionic theory, Xu gave in [14] a formal variational calculus of super-variables. Fermionic Novikov algebras are related to the Hamiltonian super-operator in terms of this theory. A fermionic Novikov algebra i...
متن کاملFree pre-Lie algebras are free as Lie algebras
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 کاملCycle-free chessboard complexes and symmetric homology of algebras
Chessboard complexes and their relatives have been an important recurring theme of topological combinatorics (see [1], [5], [10], [11], [13], [14], [20], [23], [24], [25]). Closely related “cycle-free chessboard complexes” have been recently introduced by Ault and Fiedorowicz in [2] and [9] as a tool for computing symmetric analogues of the cyclic homology of algebras. We study connectivity pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 2002
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.2002.v4.n2.a8