Modeled on work of Bott–Samelson, Soergel, and Elias–Williamson we introduce the Bott–Samelson ring $\overline{\mathrm{BS}}(s_1,s_2,\dots ,s_k)$ associated to reflections $s_1,s_2,\dots ,s_k\in \mathrm{GL}(n,\mathbb{F})$ where $\mathbb{F}$ is a field. We show that for semisimple reflections it is a complete intersection algebra with a triangular pattern of relations and has the strong Lefschetz property. For a finite nonmodular reflection group generated by reflections of order two we produce a degree one embedding of the coinvariant algebra $\mathbb{F}{[V]}_G$ into a Bott–Samelson $\overline{\mathrm{BS}}(s_1,s_2,\dots ,s_k)$ algebra where $s_1,s_2,\dots ,s_k\in G$ are reflections of order two generating G answering a question of J. Watanabe. We show by example that the strong Lefschetz property of $\overline{\mathrm{BS}}(s_1,s_2,\dots ,s_k)$ need not be inherited by the embedded $\mathbb{F}{[V]}_G$ answering another question of J. Watanabe. Finally we investigate the decomposition map

以Bott–Samelson，Soergel和Elias–Williamson的工作为模型，我们介绍了Bott–Samelson环 $\stackrel{〜}{\mathrm{学士学位}}（s_{\mathrm{1个}}，s_2，\dots ，s_{ķ}）$ 与反思相关 $s_{\mathrm{1个}}，s_2，\dots ，s_{ķ}\in \mathrm{GL}（ñ，\mathbb{F}）$ 哪里 $\mathbb{F}$是一个领域。我们表明，对于半简单反射，它是具有三角关系的完整交点代数，并具有很强的Lefschetz性质。对于由二阶反射生成的有限非模反射群，我们产生协变代数的一阶嵌入$\mathbb{F}{[V]}_G$ 进入博特-萨默森 $\stackrel{〜}{\mathrm{学士学位}}（s_{\mathrm{1个}}，s_2，\dots ，s_{ķ}）$ 代数在哪里 $s_{\mathrm{1个}}，s_2，\dots ，s_{ķ}\in G$是阶次生成G的反映，回答了渡边J.的问题。我们通过示例表明，Lefschetz的强属性$\stackrel{〜}{\mathrm{学士学位}}（s_{\mathrm{1个}}，s_2，\dots ，s_{ķ}）$ 不需要被嵌入式继承 $\mathbb{F}{[V]}_G$回答渡边J.的另一个问题。最后我们研究分解图