Weakly projective and regularly filtered algebras

1994 ◽  
pp. 111-145
Author(s):  
Lutz Heindorf ◽  
Sakaé Fuchino ◽  
Leonid B. Shapiro
Keyword(s):  
Filtered Algebras

X-Inner Automorphisms of Filtered Algebras

1981 ◽  
Vol 83 (2) ◽  
pp. 263 ◽  
Author(s):  
Susan Montgomery
Keyword(s):  
Filtered Algebras ◽  
Inner Automorphisms

On the Global Dimension of Some Filtered Algebras

1976 ◽  
Vol s2-13 (2) ◽  
pp. 239-248 ◽  
Author(s):  
S. M. Bhatwadekar
Keyword(s):  
Global Dimension ◽  
Filtered Algebras

Resolutions for some filtered algebras

1962 ◽  
Vol 148 (4) ◽  
pp. 341-348 ◽  
Author(s):  
S. Ramanan ◽  
R. Sridharan
Keyword(s):  
Filtered Algebras

Triangular Automorphisms

2017 ◽  
Author(s):  
Matthias Aschenbrenner ◽  
Lou van den Dries ◽  
Joris van der Hoeven
Keyword(s):  
Commutative Ring ◽  
Lie Algebra ◽  
Polynomial Algebra ◽  
Polynomial Rings ◽  
Differential Polynomials ◽  
Graded Algebras ◽  
Linear Maps ◽  
Unitriangular Group ◽  
Filtered Algebras ◽  
Filtered Modules

This chapter focuses on triangular automorphisms, which can be analyzed by Lie techniques. Throughout the discussion K is a commutative ring containing ℚ as a subring. A formalism is introduced to analyze triangular automorphisms of such a polynomial algebra by means of their logarithms, the triangular derivations. After presenting some definitions and simple facts about filtered modules, filtered algebras, and graded algebras, the chapter considers triangular linear maps and the Lie algebra of an algebraic unitriangular group. It then describes derivations on the ring of column-finite matrices, along with iteration matrices and Riordan matrices. It also explains derivations on polynomial rings and concludes by applying triangular automorphisms to differential polynomials.

Graded and filtered algebras and modules

1999 ◽  
pp. 61-72
Author(s):  
Günter Krause ◽  
Thomas Lenagan
Keyword(s):  
Filtered Algebras

scholarly journals Filtered algebras and representations of Lie algebras

1961 ◽  
Vol 100 (3) ◽  
pp. 530-530 ◽  
Author(s):  
R. Sridharan
Keyword(s):  
Lie Algebras ◽  
Representations Of Lie Algebras ◽  
Filtered Algebras

scholarly journals $X$-inner automorphisms of filtered algebras. II

1983 ◽  
Vol 87 (4) ◽  
pp. 569-569
Author(s):  
Susan Montgomery
Keyword(s):  
Filtered Algebras ◽  
Inner Automorphisms

Cyclic homology of filtered algebras

K-Theory ◽  
1987 ◽  
Vol 1 (5) ◽  
pp. 515-518 ◽  
Author(s):  
Jonathan L. Block
Keyword(s):  
Cyclic Homology ◽  
Filtered Algebras

scholarly journals Gelfand-Kirillov dimension of multi-filtered algebras

1999 ◽  
Vol 42 (1) ◽  
pp. 155-168 ◽  
Author(s):  
José Gómez Torrecillas
Keyword(s):  
Graded Algebra ◽  
Associative Algebras ◽  
Enveloping Algebra ◽  
Quantum Matrices ◽  
Weyl Algebras ◽  
Finite Dimensional ◽  
Ore Extensions ◽  
Filtered Algebras ◽  
Kirillov Dimension ◽  
Noetherian Algebra

We consider associative algebras filtered by the additive monoid ℕp. We prove that, under quite general conditions, the study of Gelfand-Kirillov dimension of modules over a multi-filtered algebra R can be reduced to the associated ℕp-graded algebra G(R). As a consequence, we show the exactness of the Gelfand-Kirillov dimension when the multi-filtration is finite-dimensional and G(R) is a finitely generated noetherian algebra. Our methods apply to examples like iterated Ore extensions with arbitrary derivations and “homothetic” automorphisms (e.g. quantum matrices, quantum Weyl algebras) and the quantum enveloping algebra of sl(v + 1)

X-Inner Automorphisms of Filtered Algebras. II

1983 ◽  
Vol 87 (4) ◽  
pp. 569
Author(s):  
Susan Montgomery
Keyword(s):  
Filtered Algebras ◽  
Inner Automorphisms
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