共查询到20条相似文献,搜索用时 0 毫秒
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In this paper, we study (associative) Nijenhuis algebras, with emphasis on the relationship between the category of Nijenhuis algebras and the categories of NS algebras and related algebras. This is in analogy to the well-known theory of the adjoint functor from the category of Lie algebras to that of associative algebras, and the more recent results on the adjoint functor from the categories of dendriform and tridendriform algebras to that of Rota-Baxter algebras. We first give an explicit construction of free Nijenhuis algebras and then apply it to obtain the universal enveloping Nijenhuis algebra of an NS algebra. We further apply the construction to determine the binary quadratic nonsymmetric algebra, called the N-dendriform algebra, that is compatible with the Nijenhuis algebra. As it turns out, the N-dendriform algebra has more relations than the NS algebra. 相似文献
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Kurusch Ebrahimi-Fard 《Journal of Pure and Applied Algebra》2008,212(2):320-339
In this paper we study the adjoint functors between the category of Rota-Baxter algebras and the categories of dendriform dialgebras and trialgebras. In analogy to the well-known theory of the adjoint functor between the category of associative algebras and Lie algebras, we first give an explicit construction of free Rota-Baxter algebras and then apply it to obtain universal enveloping Rota-Baxter algebras of dendriform dialgebras and trialgebras. We further show that free dendriform dialgebras and trialgebras, as represented by binary planar trees and planar trees, are canonical subalgebras of free Rota-Baxter algebras. 相似文献
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George E. Andrews Li Guo William Keigher Ken Ono 《Transactions of the American Mathematical Society》2003,355(11):4639-4656
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
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Frank Loose 《代数通讯》2013,41(7):2395-2416
Abstract A ring R is called left P-injective if for every a ∈ R, aR = r(l(a)) where l( ? ) and r( ? ) denote left and right annihilators respectively. The ring R is called left GP-injective if for any 0 ≠ a ∈ R, there exists n > 0 such that a n ≠ 0 and a n R = r(l(a n )). As a response to an open question on GP -injective rings, an example of a left GP-injective ring which is not left P-injective is given. It is also proved here that a ring R is left FP -injective if and only if every matrix ring 𝕄 n (R) is left GP-injective. 相似文献
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G. C. Wraith 《Annali di Matematica Pura ed Applicata》1967,76(1):149-163
Summary In any category with products and a terminal object one may define the notions of group, module over a group etc. if f: R′→R
is a homomorphism of groups, and M an R-module, then one has an induced R′-module f*(M). If one is working in the category
of sets, one may define a functor left adjoint to f* by N→R⊗R′ N, where N is an R′-module. In this paper we show that f* has a left adjoint when one is working in the category of graded
connected coalgebras over a field. 相似文献
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D. Jakubíková-Studenovská 《Algebra Universalis》1998,40(1):59-72
This paper deals with representations of monounary algebras by bottleneck algebras (b-representations). Necessary and sufficient
conditions for a monounary algebra to have a b-representation are found: In particular, it is shown that each finite monounary
algebra is b-representable.
Received June 25, 1997; accepted in final form June 11, 1998. 相似文献
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For a given hereditary abelian category satisfying some finiteness conditions, in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the modified Ringel-Hall algebra to the lattice algebra. Furthermore, the kernel of this epimorphism is described explicitly. Finally, we show that the naive lattice algebra is invariant under the derived equivalences of hereditary abelian categories. 相似文献
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Yanan Lin 《Advances in Mathematics》2005,196(2):487-530
This article is to study relations between tubular algebras of Ringel and elliptic Lie algebras in the sense of Saito-Yoshii. Using the explicit structure of the derived categories of tubular algebras given by Happel-Ringel, we prove that the elliptic Lie algebra of type , , or is isomorphic to the Ringel-Hall Lie algebra of the root category of the tubular algebra with the same type. As a by-product of our proof, we obtain a Chevalley basis of the elliptic Lie algebra following indecomposable objects of the root category of the corresponding tubular algebra. This can be viewed as an analogue of the Frenkel-Malkin-Vybornov theorem in which they described a Chevalley basis for each untwisted affine Kac-Moody Lie algebra by using indecomposable representations of the corresponding affine quiver. 相似文献
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Tubular algebras and affine Kac-Moody algebras 总被引:1,自引:0,他引:1
Zheng-xin CHEN & Ya-nan LIN School of Mathematics Computer Science Pujian Normal University Fuzhou China School of Mathematical Sciences Xiamen University Xiamen China 《中国科学A辑(英文版)》2007,50(4):521-532
The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules. 相似文献
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Zhi-xiang Wu 《高校应用数学学报(英文版)》2018,33(1):107-126
In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra H, and a series of weak Hopf algebras. Some results of [8] are generalized. 相似文献
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We define admissible quasi-Hopf quantized universal enveloping (QHQUE) algebras by ?-adic valuation conditions. We show that any QHQUE algebra is twist-equivalent to an admissible one. We prove a related statement: any associator is twist-equivalent to a Lie associator. We attach a quantized formal series algebra to each admissible QHQUE algebra and study the resulting Poisson algebras. 相似文献
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ABSTRACTWe describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself. 相似文献