Two Dimensional Indecomposable Modules over Infinite Dimensional Hereditary Path Algebras

Non-isomorphic two dimensional indecomposable modules over infinite dimensional hereditary path algebras are described. We infer that none of them can be determined by their dimension vectors.

Seneralized Path Algebras and Pointed Hopf Algebras

Most of pointed Hopf algebras of dimension p^m with large coradtical are shown to be generalized path algebras. By the theory of generalized path algebras, the representations, homological dimensions and radicals of these Hopf algebras are obtained. The relations between the radicals of path algebras and connectivity of directed graphs are given.

*-Regular Leavitt Path Algebras of Arbitrary Graphs

If K is a field with involution and E an arbitrary graph, the involution from K naturally induces an involution of the Leavitt path algebra LK（E）. We show that the involution on LK（E） is proper if the involution on K is positive-definite, even in the case when the graph E is not necessarily finite or row-finite. It has been shown that the Leavitt path algebra LK（E） is regular if and only if E is acyclic. We give necessary and sufficient conditions for LK（E） to be ＊-regular （i.e., regular with proper involution）. This characterization of ＊-regularity of a Leavitt path algebra is given in terms of an algebraic property of K, not just a graph-theoretic property of E. This differs from the known characterizations of various other algebraic properties of a Leavitt path algebra in terms of graph- theoretic properties of E alone. As a corollary, we show that Handelman＇s conjecture （stating that every ,-regular ring is unit-regular） holds for Leavitt path algebras. Moreover, its generalized version for rings with local units also continues to hold for Leavitt path algebras over arbitrary graphs.

Constructing cotorsion pairs over generalized path algebras

We introduce two adjoint pairs （eλ^i（）i） and （（）i,ep^i） and give a new method to construct cotorsion pairs. As applications, we characterize all projective and injective representations of a generalized path algebra and exhibit projective and injective objects of the category Mp which is a generalization of monomorphisms category.

Limiting stand density and basal area projection models for even-aged Tecomella undulata plantations in a hot arid region of India

This paper presents equations for estimating limiting stand density for Z undulata plantations grown in hot desert areas of Raj asthan State in India. Five different stand level basal area projection models, belonging to the path invariant algebraic difference form of a non-linear growth function, were also tested and compared. These models can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are necessary for reviewing different silvicultural treatment options. Data from 22 sample plots were used for modelling. An all possible growth intervals data structure was used. Both, qualitative and quantitative criteria were used to compare alternative models. The Akaike＇s information criteria differ- ence statistic was used to analyze the predictive ability of the models. Results show that the model proposed by Hui and Gadow performed best and hence this model is recommended for use in predicting basal area development in 12 undulata plantations in the study area. The data used were not from thinned stands, and hence the models may be less accurate when used for predictions when natural mortality is very significant.

On Connected Components of Skew Group Algebras

Let A be a basic connected finite dimensional associative algebra over an algebraically closed field k and G be a cyclic group.There is a quiver QGwith relationsρG such that the skew group algebras A[G]is Morita equivalent to the quotient algebra of path algebra kQGmodulo ideal(ρG).Generally,the quiver QGis not connected.In this paper we develop a method to determine the number of connect components of QG.Meanwhile,we introduce the notion of weight for underlying quiver of A such that A is G-graded and determine the connect components of smash product A#kG*.

K_1 Group of Finite Dimensional Path Algebra

In this paper, by calculating the commutator subgroup of the unit group of finite path algebra k△ and the unit group abelianized, we explicitly characterize the K1 group of finite dimensional path algebra over an arbitrary field.