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pro vyhledávání: '"GOODEARL, K A"'
Let $K$ be a field, $Q$ a quiver, and $\mathcal{A}$ the ideal of the path algebra $KQ$ that is generated by the arrows of $Q$. We present old and new results about the representation theories of the truncations $KQ/\mathcal{A}^L$, $L \in \mathbb{N}$,
Externí odkaz:
http://arxiv.org/abs/2412.12431
Autor:
Goodearl, K. R.
The article targets binomial ideals in quantum tori and quantum affine spaces. First, noncommutative analogs of known results for commutative (Laurent) polynomial rings are obtained, including the following: Under the assumption of an algebraically c
Externí odkaz:
http://arxiv.org/abs/2311.15191
Autor:
Goodearl, K. R.
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine algebraic var
Externí odkaz:
http://arxiv.org/abs/2211.14967
Autor:
Goodearl, K. R., Launois, S.
We prove that for the iterated Poisson polynomial rings known as Poisson nilpotent algebras (or Poisson-CGL extensions), the Poisson prime spectrum is catenary, i.e., all saturated chains of inclusions of Poisson prime ideals between any two given Po
Externí odkaz:
http://arxiv.org/abs/2105.13737
Autor:
Goodearl, K. R., Launois, S.
In this paper, it is established that quantum nilpotent algebras (also known as CGL extensions) are catenary, i.e., all saturated chains of inclusions of prime ideals between any two given prime ideals $P \subsetneq Q$ have the same length. This is a
Externí odkaz:
http://arxiv.org/abs/2008.01423
Autor:
Goodearl, K. R., Yakimov, M. T.
We prove a general theorem for constructing integral quantum cluster algebras over ${\mathbb{Z}}[q^{\pm 1/2}]$, namely that under mild conditions the integral forms of quantum nilpotent algebras always possess integral quantum cluster algebra structu
Externí odkaz:
http://arxiv.org/abs/2003.04434
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Tauvel's height formula, which provides a link between the height of a prime ideal and the Gelfand-Kirillov dimension of the corresponding factor algebra, is verified for quantum nilpotent algebras.
Externí odkaz:
http://arxiv.org/abs/1805.06590
Publikováno v:
in Geometric and Topological Aspects of the Representation Theory of Finite Groups (J. Carlson, S. Iyengar and J. Pevtsova, Eds.), Springer Proc. Math. Stat. 242, Springer (2018) Cham, pp. 131-179
We survey the development and status quo of a subject best described as "generic representation theory of finite dimensional algebras", which started taking shape in the early 1980s. Let $\Lambda$ be a finite dimensional algebra over an algebraically
Externí odkaz:
http://arxiv.org/abs/1801.09169
Publikováno v:
Algebra and Number Theory 12 (2018) 379-410
For any truncated path algebra $\Lambda$ of a quiver, we classify, by way of representation-theoretic invariants, the irreducible components of the parametrizing varieties $\mathbf{Rep}_{\mathbf{d}}(\Lambda)$ of the $\Lambda$-modules with fixed dimen
Externí odkaz:
http://arxiv.org/abs/1801.09168